symmetries of the turbulent state the emphasis of this review is on fundamental properties degree of universality and symmetries of the turbulent state the central questions are which symmetries remain broken even when the symmetry breaking factor reaches zero and which symmetries in contrast emerge in the state of developed turbulence we shall see that time reversibility is broken in all cases since turbulence is a far from equilibrium state accompanied by dissipation as far as scale invariance is concerned we argue that it is always broken in direct cascades toward small scales no matter how far one goes away from the pumping scale in contrast inverse cascades become scale invariant as they go toward large scales moreover some properties of the inverse cascades seem to be conformal invariant and related to schramm loewner evolution a class of random curves that can be mapped to a 1d brownian walk

existence and regularity of invariant measures for the three dimensional stochastic primitive equations we establish the continuity of the markovian semigroup associated with strong solutions of the stochastic 3d primitive equations and prove the existence of an invariant measure the proof is based on new moment bounds for strong solutions the invariant measure is supported on strong solutions and is furthermore shown to have higher regularity properties

mean field approximation and a small parameter in turbulence theory numerical and physical experiments on two dimensional 2d turbulence show that the differences of transverse components of velocity field are well described by gaussian statistics and kolmogorov scaling exponents in this case the dissipation fluctuations are irrelevant in the limit of small viscosity in general one can assume the existence of a critical space dimensionality d d c at which the energy flux and all odd order moments of velocity difference change sign and the dissipation fluctuations become dynamically unimportant at dl d c the flow can be described by the mean field theory leading to the observed gaussian statistics and kolmogorov scaling of transverse velocity differences it is shown that in the vicinity of d d c the ratio of the relaxation and translation characteristic times decreases to zero thus giving rise to a small parameter of the theory the expressions for pressure and dissipation contributions to the exact equation for the generating function of transverse velocity differences are derived in the vicinity of d d c the resulting equation describes experimental data on two dimensional turbulence and demonstrates the onset of intermittency as d ensuremath d c g0 and r stackrel ensuremath rightarrow l 0 in three dimensional flows in close agreement with experimental data in addition some exact relations between correlation functions of velocity differences are derived it is also predicted that the single point probability density function of transverse velocity components in developing as well as in the large scale stabilized two dimensional turbulence is a gaussian

on crank nicolson adams bashforth timestepping for approximate deconvolution models in two dimensions we consider a crank nicolson adams bashforth temporal discretization together with a finite element spatial discretization for efficiently computing solutions to approximate deconvolution models of incompressible flow in two dimensions we prove a restriction on the timestep that will guarantee stability and provide several numerical experiments that show the proposed method is very effective at finding accurate coarse mesh approximations for benchmark flow problems

a coarse grid projection method for accelerating incompressible flow computations we present a coarse grid projection cgp method for accelerating incompressible flow computations which is applicable to methods involving poisson equations as incompressibility constraints the cgp methodology is a modular approach that facilitates data transfer with simple interpolations and uses black box solvers for the poisson and advection diffusion equations in the flow solver after solving the poisson equation on a coarsened grid an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid a particular version of the method is applied here to the vorticity stream function primitive variable and vorticity velocity formulations of incompressible navier stokes equations we compute several benchmark flow problems on two dimensional cartesian and non cartesian grids as well as a three dimensional flow problem the method is found to accelerate these computations while retaining a level of accuracy close to that of the fine resolution field which is significantly better than the accuracy obtained for a similar computation performed solely using a coarse grid a linear acceleration rate is obtained for all the cases we consider due to the linear cost elliptic poisson solver used with reduction factors in computational time between 2 and 42 the computational savings are larger when a suboptimal poisson solver is used we also find that the computational savings increase with increasing distortion ratio on non cartesian grids making the cgp method a useful tool for accelerating generalized curvilinear incompressible flow solvers

temporal multiscaling in hydrodynamic turbulence on the basis of the navier stokes equations we develop the high reynolds number statistical theory of different time many point spatial correlation functions of velocity differences we find that their time dependence is not scale invariant n order correlation functions exhibit infinitely many distinct decorrelation times that are characterized by anomalous dynamical scaling exponents we derive exact scaling relations that bridge all these dynamical exponents to the static anomalous exponents mathrm ensuremath zeta mathrm q of the standard structure functions we propose a representation of the time dependence using the legendre transform formalism of multifractals that automatically reproduces all the newly found bridge relationships

adaptive tracking control of a class of uncertain chaotic systems in the presence of random perturbations considering the effect of random perturbations on the chaotic system a new adaptive tracking control is presented for a large class of uncertain chaotic systems using the invariance principle of differential equations where the bound of random perturbations is not necessarily known in advance and it is estimated through an adaptive control process it is theoretically proved that this approach can make the perturbed chaotic system track any desired reference signal in addition we can see that this method can apply to almost all uncertain chaotic systems and it is simpler and easier to implement in practical application in the end we take the perturbed lorenz system as an example to illustrate that the proposed scheme is effective

a modified fuzzy c means algorithm for bias field estimation and segmentation of mri data we present a novel algorithm for fuzzy segmentation of magnetic resonance imaging mri data and estimation of intensity inhomogeneities using fuzzy logic mri intensity inhomogeneities can be attributed to imperfections in the radio frequency coils or to problems associated with the acquisition sequences the result is a slowly varying shading artifact over the image that can produce errors with conventional intensity based classification our algorithm is formulated by modifying the objective function of the standard fuzzy c means fcm algorithm to compensate for such inhomogeneities and to allow the labeling of a pixel voxel to be influenced by the labels in its immediate neighborhood the neighborhood effect acts as a regularizer and biases the solution toward piecewise homogeneous labelings such a regularization is useful in segmenting scans corrupted by salt and pepper noise experimental results on both synthetic images and mr data are given to demonstrate the effectiveness and efficiency of the proposed algorithm

fully developed isotropic turbulence symmetries and exact identities we consider the regime of fully developed isotropic and homogeneous turbulence of the navier stokes equation with a stochastic forcing we present two gauge symmetries of the corresponding navier stokes field theory and derive the associated general ward identities furthermore by introducing a local source bilinear in the velocity field we show that these symmetries entail an infinite set of exact and local relations between correlation functions they include in particular the k arm an howarth relation and another exact relation for a pressure velocity correlation function recently derived in g falkovich i fouxon and y oz j fluid mech 644 465 2010 that we further generalize

frame invariance and conservation in two dimensional subgrid models abstract we explore how symmetry and conservation requirements affect the form of subgrid models in large eddy simulations les of two dimensional incompressible turbulence we expose two possible strategies that can be adopted in order to preserve these symmetries in the two dimensional case a representational approach where the invariance properties are taken as the basic ingredient guiding the formulation of the model and the variational euler poincare procedure where the invariance properties are a built in feature of the resulting euler equations assuming spatial locality we find that at leading order in spatial derivatives of the resolved velocity field the only compatible model is the strain diffusivity model formal analogies between the euler model and the strain diffusivity model allow us to derive a new model with conservation properties presumably more suited to the two dimensional situation in this process the strain diffusivity operator appears as a truncated version of both euler and models the numerical properties of the three considered models are estimated and discussed

ergodic and mixing properties of the boussinesq equations with a degenerate random forcing we establish the existence uniqueness and attraction properties of an ergodic invariant measure for the boussinesq equations in the presence of a degenerate stochastic forcing acting only in the temperature equation and only at the largest spatial scales the central challenge is to establish time asymptotic smoothing properties of the markovian dynamics corresponding to this system towards this aim we encounter a lie bracket structure in the associated vector fields with a complicated dependence on solutions this leads us to develop a novel hormander type condition for infinite dimensional systems demonstrating the sufficiency of this condition requires new techniques for the spectral analysis of the malliavin covariance matrix

nonlinear transfer and spectral distribution of energy in α turbulence abstract two dimensional turbulence governed by the so called turbulence equations which include the surface quasi geostrophic equation 1 the navier stokes system 2 and the governing equation for a shallow flow on a rotating domain driven by a uniform internal heating 3 is studied here in both the unbounded and doubly periodic domains this family of equations conserves two inviscid invariants energy and enstrophy in the navier stokes case the dynamics of which are believed to undergo a dual cascade it is shown that an inverse cascade can exist in the absence of a direct cascade and that the latter is possible only when the inverse transfer rate of the inverse cascading quantity approaches its own injection rate constraints on the spectral exponents in the wavenumber ranges lower and higher than the injection range are derived for navier stokes turbulence with moderate reynolds numbers the realization of an inverse energy cascade in the complete absence of a direct enstrophy cascade is confirmed by numerical simulations

an extension of the standard mixture model for image segmentation standard gaussian mixture modeling gmm is a well known method for image segmentation however the pixels themselves are considered independent of each other making the segmentation result sensitive to noise to reduce the sensitivity of the segmented result with respect to noise markov random field mrf models provide a powerful way to account for spatial dependences between image pixels however their main drawback is that they are computationally expensive to implement and require large numbers of parameters based on these considerations we propose an extension of the standard gmm for image segmentation which utilizes a novel approach to incorporate the spatial relationships between neighboring pixels into the standard gmm the proposed model is easy to implement and compared with mrf models requires lesser number of parameters we also propose a new method to estimate the model parameters in order to minimize the higher bound on the data negative log likelihood based on the gradient method experimental results obtained on noisy synthetic and real world grayscale images demonstrate the robustness accuracy and effectiveness of the proposed model in image segmentation as compared to other methods based on standard gmm and mrf models

locality and stability of the cascades of two dimensional turbulence we investigate and clarify the notion of locality as it pertains to the cascades of two dimensional turbulence the mathematical framework underlying our analysis is the infinite system of balance equations that govern the generalized unfused structure functions first introduced by l vov and procaccia as a point of departure we use a revised version of the system of hypotheses that was proposed by frisch for three dimensional turbulence we show that both the enstrophy cascade and the inverse energy cascade are local in the sense of non perturbative statistical locality we also investigate the stability conditions for both cascades we have shown that statistical stability with respect to forcing applies unconditionally for the inverse energy cascade for the enstrophy cascade statistical stability requires large scale dissipation and a vanishing downscale energy dissipation a careful discussion of the subtle notion of locality is given at the end of the paper

anomalous scaling in homogeneous isotropic turbulence the anomalous scaling exponents n of the longitudinal structure functions sn for homogeneous isotropic turbulence are derived from the navier stokes equations by using field theoretic methods to develop a low energy approximation in which the kolmogorov theory is shown to act effectively as a mean field theory the corrections to the kolmogorov exponents are expressed in terms of the anomalous dimensions of the composite operators which occur in the definition of sn these are calculated from the anomalous scaling of the appropriate class of nonlinear green function using an uv fixed point of the renormalization group which thereby establishes the connection with the dynamics of the turbulence the main result is an algebraic expression for n which contains no adjustable constants it is valid at orders n below g 1 where g is the fixed point coupling constant this expression is used to calculate n for orders in the range n 2 10 and the results are shown to be in good agreement with experimental data key examples being 2 0 7 3 1 and 6 1 8

exact resummations in the theory of hydrodynamic turbulence iii scenarios for anomalous scaling and intermittency elements of the analytic structure of anomalous scaling and intermittency in fully developed hydrodynamic turbulence are described we focus here on the structure functions of velocity differences that satisfy inertial range scaling laws s n r sim r zeta n and the correlation of energy dissipation k epsilon epsilon r sim r mu the goal is to understand the exponents zeta n and mu from first principles in paper ii of this series it was shown that the existence of an ultraviolet scale the dissipation scale eta is associated with a spectrum of anomalous exponents that characterize the ultraviolet divergences of correlations of gradient fields the leading scaling exponent in this family was denoted delta the exact resummation of ladder diagrams resulted in the calculation of delta which satisfies the scaling relation delta 2 zeta 2 in this paper we continue our analysis and show that nonperturbative effects may introduce multiscaling i e zeta n not being linear in n with the renormalization scale being the infrared outer scale of turbulence l it is shown that deviations from k41 scaling of s n r zeta n neq n 3 must appear if the correlation of dissipation is mixing i e mu 0 we derive an exact scaling relation mu 2 zeta 2 zeta 4 we present analytic expressions for zeta n for all n and discuss their relation to experimental data one surprising prediction is that the time decay constant tau n r propto r z n of s n r scales independently of n the dynamic scaling exponent z n is the same for all n order quantities z n zeta 2

locality of turbulent cascades in this paper we establish sufficient conditions for locality of turbulent cascades by an exact analysis of the fluid equations no assumptions of homogeneity or isotropy are invoked and the results apply to individual realizations with no resort to any statistical averaging the only requirement is suitable regularity of the turbulent solutions of the fluid equations in the high reynolds number limit corresponding to holder continuity but non differentiability in space we use a smooth filtering approach to resolve the turbulent fields both in space and in scale we discuss several physical cascades to exemplify and clarify the analysis including joint energy and helicity cascades in three space dimensions and the dual inverse energy cascade and direct enstrophy cascade in two dimensions

the use of explicit filters in large eddy simulation abstract explicit filtering is considered as a means of controlling the numerical errors that result when finite difference methods are used in large eddy simulation les the notion that the finite difference expressions themselves act as an effective filter is shown to be false for three dimensional simulations performed on nonuniform meshes for consistency the nonlinear terms in the navier stokes equations should be filtered explicitly at each time step in order to insure that the spectral content of the solution remains fixed at the desired filter level the explicit filtering operation allows a separation between the filter size and the mesh spacing and can be used to control the impact of the numerical errors numerical tests of the explicit filtering approach in turbulent channel flow are used to investigate the effectiveness of the explicit filtering approach and to assess its associated cost explicit filtering is shown to improve the computed results but this improvement comes at a rather high computational cost the explicitly filtered approach is also compared with straightforward mesh refinement as an alternative means of improving the computed results mesh refinement is also seen to increase the accuracy of the simulation but some traces of numerical error appear to persist in the solution

onsager s conjecture on the energy conservation for solutions of euler s equation we give a simple proof of a result conjectured by onsager 1 on energy conservation for weak solutions of euler s equation

large eddy simulation of turbulent obstacle flow using a dynamic subgrid scale model we apply the dynamic subgrid scale model to a large eddy simulation of turbulent channel flow with a square rib mounted on one wall the reynolds number re is 3 21 x 10 3 based on the mean velocity above the obstacle and the obstacle s height near wall structures are resolved with the no slip boundary condition the results show better agreement with direct numerical simulation than large eddy simulation with a fixed model constant verifying the value of the dynamic subgrid scale model for simulating complex turbulent flows arge eddy simulation les is an accurate method of simulating complex turbulent flows in which the large flow structures are computed while small scales are modeled the rationale behind this method is based on two observations most of the turbulent energy is in the large structures and the small scales are more isotropic and universal therefore les may be more general and less geometry dependent than reynolds averaged modeling although it comes at higher cost even though les has been used by many investigators most research has been limited to flows with simple geometry in engineering applications however one encounters more complicated geometries here we shall consider a rectangular parallelepiped mounted on a flat surface related flows are those over surfaces protruding from submarines conning towers or control fins wind flows around buildings and airflows over computer chips among others the most distinctive features associated with these flows are three dimensionality flow separation due to protruding surfaces and large scale unsteadiness as a model flow we consider a plane channel flow in which a two dimensional obstacle is mounted on one surface see fig 1 this relatively simple geometry contains flow separation and reattachment flow in this geometry has been studied by tropea and gackstatter1 for low re and werner and wengle2 and dimaczek et al 3 for high re among others recently germano et al 4 suggested a dynamic subgridscale model dsgsm in which the model coefficient is dynamically computed as computation progresses rather than specified a priori this approach is based on an algebraic identity between the subgrid scale stresses at two different filter levels and the resolved turbulent stresses they applied the model to transitional and fully turbulent channel flows and showed that the model contributes nothing in laminar flow and exhibits the correct asymptotic behavior in the nearwall region of turbulent flows without an ad hoc damping function this is a significant improvement over conventional subgrid scale modeling

computing the scaling exponents in fluid turbulence from first principles the formal setup abstract we propose a scheme for the calculation from the navier stokes equations of the scaling exponents n of the nth order correlation functions in fully developed hydrodynamic turbulence the scheme is nonperturbative and constructed to respect the fundamental rescaling symmetry of the euler equation it constitutes an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents n as a consequence the scaling exponents are determined by solvability conditions and not from power counting it is argued that in order to achieve such a formulation one must recognize that the many point space time correlation functions are not scale invariant in their time arguments the assumption of full scale invariance leads unavoidably to kolmogorov exponents it is argued that the determination of all the scaling exponents n requires equations for infinitely many renormalized objects one can however proceed in controlled successive approximations by successive truncations of the infinite hierarchy of equations clues as to how to truncate without reintroducing power counting can be obtained from renormalized perturbation theory to this aim we show that the fully resummed perturbation theory is equivalent in its contents to the exact hierarchy of equations obeyed by the nth order correlation functions and green s function in light of this important result we can safely use finite resummations to construct successive closures of the infinite hierarchy of equations this paper presents the conceptual and technical details of the scheme the analysis of the high order closure procedures which do not destroy the rescaling symmetry and the actual calculations for truncated models will be presented in a forthcoming paper in collaboration with v belinicher

universal direct cascade in two dimensional turbulence we consider the correlation functions of vorticity ensuremath omega in the region of the direct cascade in a steady two dimensional turbulence the nonlocality of the cascade in k space provides for logarithmic corrections to the expressions obtained by dimension estimates and the main problem is to take those logarithms into account our procedure starts directly with the euler equation rewritten in the comoving reference frame we express the correlation functions of the vorticity via the correlation functions of the pumping force and renormalized strain it enables us to establish a set of integrodifferential equations which gives a logarithmic renormalization of the vorticity correlation functions in the inertial interval we find the indices characterizing the logarithmic behavior of different correlation functions for example the two point simultaneous functions are as follows mathrm ensuremath omega mathit n mathbf r 1 mathrm ensuremath omega mathit n mathbf r 2 ensuremath sim mathit p 2 ln l mathbf r 1 mathbf r 2 ensuremath vert 2 mathit n 3 where l is the pumping scale we demonstrate that the form of those correlation functions is universal i e independent of the pumping the only pumping related value which enters the expressions is the enstrophy production rate mathit p 2 the contributions related to pumping rates mathit p mathit n of the higher order integrals of motion are demonstrated to be small in comparison with the ones induced by mathit p 2 we establish also the time dependence of the correlation functions the correlation time ensuremath tau in the comoving reference frame is the same for the vorticity and strain and is scale dependent ensuremath tau ensuremath propto mathrm ln 2 3 l r we reformulate our procedure in the diagrammatic language to reinforce the conclusions

a spatially constrained mixture model for image segmentation gaussian mixture models gmms constitute a well known type of probabilistic neural networks one of their many successful applications is in image segmentation where spatially constrained mixture models have been trained using the expectation maximization em framework in this letter we elaborate on this method and propose a new methodology for the m step of the em algorithm that is based on a novel constrained optimization formulation numerical experiments using simulated images illustrate the superior performance of our method in terms of the attained maximum value of the objective function and segmentation accuracy compared to previous implementations of this approach

probabilistic estimates for the two dimensional stochastic navier stokes equations we consider the navier stokes equation on a two dimensional torus with a random force white noise in time and analytic in space for arbitrary reynolds number r we prove probabilistic estimates for the long time behavior of the solutions that imply bounds for the dissipation scale and energy spectrum as r

on the dual cascade in two dimensional turbulence we study the dual cascade scenario for two dimensional turbulence driven by a spectrally localized forcing applied over a finite wavenumber range kmin kmax with kmin 0 such that the respective energy and enstrophy injection rates and satisfy k 2 k 2 the classical kraichnan leith batchelor paradigm based on the simultaneous conservation of energy and enstrophy and the scaleselectivity of the molecular viscosity requires that the domain be unbounded in both directions for two dimensional turbulence either in a doubly periodic domain or in an unbounded channel with a periodic boundary condition in the acrosschannel direction a direct enstrophy cascade is not possible in the usual case where the forcing wavenumber is no greater than the geometric mean of the integral and dissipation wavenumbers constant spectral slopes must satisfy 5 and 8 where is the asymptotic slope of the range of wavenumbers lower higher than the forcing wavenumber the influence of a large scale dissipation on the realizability of a dual cascade is analyzed we discuss the consequences for numerical simulations attempting to mimic the classical unbounded picture in a bounded domain

universal bounds on the attractor of the navier stokes equation in the energy enstrophy plane we continue our examination of the projection of the global attractor of the two dimensional navier stokes equations in a normalized dimensionless energy enstrophy plane in this plane the attractor must lie above the line of slope 1 through the origin an immediate consequence of the poincare inequality we showed in dascaliuc et al j dyn differ equ 17 629 649 2005 that the attractor must also lie below a parabola the square root curve here we optimize this parabola to obtain a sharper bound these bounds are universal they are independent of viscosity domain size and strength of the force the effectiveness of the bounds is demonstrated on galerkin approximations of modest size up to 1372 modes

a new high order energy and enstrophy conserving arakawa like jacobian differential operator a new high order arakawa like method for the incompressible vorticity equation in two dimensions has been developed mimetic properties such as skew symmetry energy and enstrophy conservations for the semi discretization are proved for periodic problems using arbitrary high order summation by parts operators numerical simulations corroborate the theoretical findings

exact results for conditional means of a passive scalar in certain statistically homogeneous flows for a passive scalar t r t randomly advected by a statistically homogeneous flow the probability density function pdf of its fluctuation can in general be expressed in terms of two conditional means 2 t t and t 2 t we find that in some special cases either one of the two conditional means can be obtained explicitly from the equation of motion in the cases when there is no external source and that the normalized fluctuation reaches a steady state or when a steady state results from a negative damping 2 t t t 2 t 2 t the linearity of the conditional mean in these cases follows directly from the fact that the advection equation of a passive scalar is linear on the other hand when the scalar is supported by a homogeneous white in time external source t 2 t t 2

segmentation of brain mr images through a hidden markov random field model and the expectation maximization algorithm the finite mixture fm model is the most commonly used model for statistical segmentation of brain magnetic resonance mr images because of its simple mathematical form and the piecewise constant nature of ideal brain mr images however being a histogram based model the fm has an intrinsic limitation no spatial information is taken into account this causes the fm model to work only on well defined images with low levels of noise unfortunately this is often not the the case due to artifacts such as partial volume effect and bias field distortion under these conditions fm model based methods produce unreliable results here the authors propose a novel hidden markov random field hmrf model which is a stochastic process generated by a mrf whose state sequence cannot be observed directly but which can be indirectly estimated through observations mathematically it can be shown that the fm model is a degenerate version of the hmrf model the advantage of the hmrf model derives from the way in which the spatial information is encoded through the mutual influences of neighboring sites although mrf modeling has been employed in mr image segmentation by other researchers most reported methods are limited to using mrf as a general prior in an fm model based approach to fit the hmrf model an em algorithm is used the authors show that by incorporating both the hmrf model and the em algorithm into a hmrf em framework an accurate and robust segmentation can be achieved more importantly the hmrf em framework can easily be combined with other techniques as an example the authors show how the bias field correction algorithm of guillemaud and brady 1997 can be incorporated into this framework to achieve a three dimensional fully automated approach for brain mr image segmentation

local energy flux and the refined similarity hypothesis in this paper we demonstrate the locality of energy transport for incompressible euler equations both in space and in scale the key to the proof is the proper definition of a local subscale flux t r which is supposed to be a measure of energy transfer to length scales l at the space point r kraichnan suggested that for such a quantity the refined similarity hypothesis will hold which kolmogorov originally assumed to hold instead for volume averaged dissipation we derive a local energy balance relation for the large scale motions which yields a natural definition of such a subscale flux for this definition a precise form of the refined similarity hypothesis is rigorously proved as a big o bound the established estimate is t r o l3h 1 in terms of the local holder exponenth at the point r which is also the estimate assumed in the parisi frisch multifractal model our method not only establishes locality of energy transfer but it also clarifies the physical reason that convection effects which naively violate locality do not contribute to the subscale flux in fact we show that as a consequence of incompressibility such effects enter into the local energy balance only as the divergence of a spatial current therefore they describe motion of energy in space and cancel in the integration over volume we also discuss theorems of onsager eyink and constantinet al on energy conservation for euler dynamics particularly to explain their relation with the parisi frisch model the constantinet al proof may be interpreted as giving a bound on the total flux t d d r t r of the form t r o lz3h 1 wherez3 is the third order scaling exponent or besov index in agreement with the multifractal model finally we discuss how the local estimates are related to the results of caffarelli kohn nirenberg on partial regularity for solutions of navier stokes equations they provide some heuristic support to a scenario proposed recently by pumir and siggia for singularities in the solutions of navier stokes with small enough viscosity

two dimensional turbulence in the inverse cascade range numerical and physical experiments on forced two dimensional navier stokes equations show that transverse velocity differences are described by normal kolmogorov scaling proportional r 2n 3 and obey gaussian statistics since nontrivial scaling is a sign of the strong nonlinearity of the problem these two results seem to contradict each other a theory explaining these observations is presented in this paper the derived self consistent expression for the pressure gradient contributions leads to the conclusion that small scale transverse velocity differences are governed by a linear langevin like equation stirred by a nonlocal universal solution dependent gaussian random force this explains the experimentally observed gaussian statistics of transverse velocity differences and their kolmogorov scaling the solution for the pdf of longitudinal velocity differences is based on the numerical smallness of the energy flux in two dimensional turbulence the theory makes a few quantitative predictions that can be tested experimentally

evidence for the double cascade scenario in two dimensional turbulence statistical features of homogeneous isotropic two dimensional turbulence is discussed on the basis of a set of direct numerical simulations up to the unprecedented resolution 32768 2 by forcing the system at intermediate scales narrow but clear inertial ranges develop both for the inverse and for direct cascades where the two kolmogorov laws for structure functions are simultaneously observed the inverse cascade spectrum is found to be consistent with kolmogorov kraichnan prediction and is robust with respect the presence of an enstrophy flux the direct cascade is found to be more sensible to finite size effects the exponent of the spectrum has a correction with respect theoretical prediction which vanishes by increasing the resolution

exact results on stationary turbulence in 2d consequences of vorticity conservation we establish a series of exact results for a model of stationary turbulence in two dimensions the incompressible navier stokes equation in a periodic domain with stochastic force white noise in time essentially all of our conclusions follow from the simple consideration of the simultaneous conservation of energy and enstrophy by the inertial dynamics our main results are as follows 1 we show the blow up of mean energy as l02e for 0 when there is no ir dissipation at the large length scale l0 2 with an additional ir dissipation we establish the validity of the traditional cascade directions and magnitudes of flux of energy and enstrophy for 0 assuming finite mean energy in the limit 3 we rigorously establish the balance equations for the energy and vorticity invariants in the 2d steady state and the forward cascade of the higher order vorticity invariants assuming finite mean values 4 we derive exact inequalities for scaling exponents in the 2d enstrophy range as follows if l p l p then 2 23 and p 0 for p 3 if the minimum holder exponent of the vorticity hmin 0 then we establish a 2d analogue of the refined similarity hypothesis which improves these bounds the most novel and interesting conclusion of this work is the connection established between intermittency in 2d and negative holder singularities of the vorticity we show that the latter are necessary for deviations from the 1967 kraichnan scaling to occur

power law correlated processes with asymmetric distributions motivated by the fact that many physical systems display sid power law correlations together with siid an asymmetry in the probability distribution we propose a stochastic process that can model both properties the process depends on only two parameters where one controls the scaling exponent of the power law correlations and the other controls the degree of asymmetry in the distributions leaving the correlations unaffected we apply the process to air humidity data and find that the statistical properties of the process are in a good agreement with those observed in the data

dynamical equations for high order structure functions and a comparison of a mean field theory with experiments in three dimensional turbulence two recent papers v yakhot phys rev e 63 026307 2001 and r j hill j fluid mech 434 379 2001 derive through two different approaches that have the navier stokes equations as the common starting point a set of dynamic equations for structure functions of arbitrary order in turbulence these equations are not closed yakhot proposed a mean field theory to close the equations for locally isotropic turbulence and obtained scaling exponents of structure functions and expressions for the peak in the probability density function of transverse velocity increments and for its behavior for intermediate amplitudes at high reynolds numbers some relevant experimental data on pressure gradient and dissipation terms are presented that are needed to provide closure as well as on other aspects predicted by the theory comparison between the theory and the data shows varying levels of agreement and reveals gaps inherent to the implementation of the theory

fully developed isotropic turbulence nonperturbative renormalization group formalism and fixed point solution we investigate the regime of fully developed homogeneous and isotropic turbulence of the navier stokes ns equation in the presence of a stochastic forcing using the nonperturbative functional renormalization group nprg within a simple approximation based on symmetries we obtain the fixed point solution of the nprg flow equations that corresponds to fully developed turbulence both in d 2 and 3 dimensions deviations to the dimensional scalings kolmogorov in d 3 or kraichnan batchelor in d 2 are found for the two point functions to further analyze these deviations we derive exact flow equations in the large wave number limit and show that the fixed point does not entail the usual scale invariance thereby identifying the mechanism for the emergence of intermittency within the nprg framework the purpose of this work is to provide a detailed basis for nprg studies of ns turbulence the determination of the ensuing intermittency exponents is left for future work

disturbance attenuation using proportional integral observers in this paper we first propose a proportional integral observer design for single output uncertain linear systems which permit us to attenuate either measurement noise or modelling errors we show that when only sensor noise is present in the system an integral observer alone suffices to achieve good convergence and filtering properties on the other hand when modelling errors and sensor noise are present we show that for some classes of linear systems the proportional integral observer allows us to decouple completely the modelling uncertainties while keeping satisfactory convergence properties a comparison of the classical proportional observer to the proposed observers are given via academic simulation examples we next extend the design to the class of single output uniformly observable non linear systems we show through a practical simulation example dealing with a flexible joint robot that the non linear proportional integral has very satisfactory disturbance attenuating properties

incorporating mean template into finite mixture model for image segmentation the well known finite mixture model fmm has been regarded as a useful tool for image segmentation application however the pixels in fmm are considered independent of each other and the spatial relationship between neighboring pixels is not taken into account these limitations make the fmm more sensitive to noise in this brief we propose a simple and effective method to make the traditional fmm more robust to noise with the help of a mean template fmm can be considered a linear combination of prior and conditional probability from the expression of its mathematical formula we calculate these probabilities with two mean templates a weighted arithmetic mean template and a weighted geometric mean template thus in our model the prior probability or conditional probability of an image pixel is influenced by the probabilities of pixels in its immediate neighborhood to incorporate the local spatial and intensity information for eliminating the noise finally our algorithm is general enough and can be extended to any other fmm based models to achieve super performance experimental results demonstrate the improved robustness and effectiveness of our approach

a non perturbative approach to critical dynamics this paper is devoted to a non perturbative renormalization group nprg analysis of model a which stands as a paradigm for the study of critical dynamics the nprg formalism has appeared as a valuable theoretical tool to investigate non equilibrium critical phenomena yet the simplest and nontrivial models for critical dynamics have never been studied using nprg techniques in this paper we focus on model a taking this opportunity to provide a pedagogical introduction to nprg methods for dynamical problems in statistical physics the dynamical exponent z is computed in d 3 and d 2 and is found to be in close agreement with results from other methods

maximum likelihood parameter estimation for unsupervised stochastic model based image segmentation an unsupervised stochastic model based approach to image segmentation is described and some of its properties investigated in this approach the problem of model parameter estimation is formulated as a problem of parameter estimation from incomplete data and the expectation maximization em algorithm is used to determine a maximum likelihood ml estimate previously the use of the em algorithm in this application has encountered difficulties since an analytical expression for the conditional expectations required in the em procedure is generally unavailable except for the simplest models in this paper two solutions are proposed to solve this problem a monte carlo scheme and a scheme related to besag s 1986 iterated conditional mode icm method both schemes make use of markov random field modeling assumptions examples are provided to illustrate the implementation of the em algorithm for several general classes of image models experimental results on both synthetic and real images are provided

on the elimination of the sweeping interactions from theories of hydrodynamic turbulence in this paper we revisit the claim that the eulerian and quasi lagrangian same time correlation tensors are equal this statement allows us to transform the results of an msr quasi lagrangian statistical theory of hydrodynamic turbulence back to the eulerian representation we define a hierarchy of homogeneity symmetries between incremental homogeneity and global homogeneity it is shown that both the elimination of the sweeping interactions and the derivation of the 4 5 law require a homogeneity assumption stronger than incremental homogeneity but weaker than global homogeneity the quasi lagrangian transformation on the other hand requires an even stronger homogeneity assumption which is many time rather than one time but still weaker than many time global homogeneity we argue that it is possible to relax this stronger assumption and still preserve the conclusions derived from theoretical work based on the quasi lagrangian transformation

lagrangian statistics in forced two dimensional turbulence we report on simulations of two dimensional turbulence in the inverse energy cascade regime focusing on the statistics of lagrangian tracer particles scaling behavior of the probability density functions of velocity fluctuations is investigated the results are compared to the three dimensional case in particular an analysis in terms of compensated cumulants reveals the transition from a strong non gaussian behavior with large tails to gaussianity the reported computation of correlation functions for the acceleration components sheds light on the underlying dynamics of the tracer particles

besov spaces and the multifractal hypothesis parisi and frisch proposed some time ago an explanation for multiscaling of turbulent velocity structure functions in terms of a multifractal hypothesis i e they conjecture that the velocity field has local holder exponents in a range hmin hmax with exponents h occurring on a sets h with a fractal dimensiond h heuristic reasoning led them to an expression for the scaling exponentz p ofpth order as the legendre transform of the codimensiond d h we show here that a part of the multifractal hypothesis is correct under even weaker assumptions namely if the velocity field hasl p mean holder indexs i e if it lies in the besov spaceb p s then local holder regularity is satisfied ifs d p then the hypothesis is true in a generalized sense of holder space with negative exponents and we discuss the proper definition of local holder classes of negative index finally if a certain box counting dimension exists then the legendre transform of its codimension gives the scaling exponentz p and more generally the maximal besov index of order p ass p z p p our method of proof is derived from a recent paper of s jaffard using compactly supported orthonormal wavelet bases and gives an extension of his results we discuss implications of the theorems for ensemble average scaling and fluid turbulence

computational design for long term numerical integration of the equations of fluid motion the integral constraints on quadratic quantities of physical importance such as conservation of mean kinetic energy and mean square vorticity will not be maintained in finite difference analogues of the equation of motion for two dimensional incompressible flow unless the finite difference jacobian expression for the advection term is restricted to a form which properly represents the interaction between grid points as derived in this paper it is shown that the derived form of the finite difference jacobian prevents nonlinear computational instability and thereby permits long term numerical integrations

multilocality and fusion rules on the generalized structure functions in two dimensional and three dimensional navier stokes turbulence using the fusion rules hypothesis for three dimensional and two dimensional navier stokes turbulence we generalize a previous nonperturbative locality proof to multiple applications of the nonlinear interactions operator on generalized structure functions of velocity differences we call this generalization of nonperturbative locality to multiple applications of the nonlinear interactions operator multilocality the resulting cross terms pose a new challenge requiring a new argument and the introduction of a new fusion rule that takes advantage of rotational symmetry our main result is that the fusion rules hypothesis implies both locality and multilocality in both the ir and uv limits for the downscale energy cascade of three dimensional navier stokes turbulence and the downscale enstrophy cascade and inverse energy cascade of two dimensional navier stokes turbulence we stress that these claims relate to nonperturbative locality of generalized structure functions on all orders and not the term by term perturbative locality of diagrammatic theories or closure models that involve only two point correlation and response functions

turbulence without pressure we develop exact field theoretic methods to treat turbulence when the effect of pressure is negligible we find explicit forms of certain probability distributions demonstrate that the breakdown of galilean invariance is responsible for intermittency and establish the operator product expansion we also indicate how the effects of pressure can be turned on perturbatively

inverse energy cascade in two dimensional turbulence deviations from gaussian behavior high resolution numerical simulations of stationary inverse energy cascade in two dimensional turbulence are presented deviations from gaussian behavior of velocity differences statistics are quantitatively investigated the level of statistical convergence is pushed enough to permit reliable measurement of the asymmetries in the probability distribution functions of longitudinal increments and odd order moments which bring the signature of the inverse energy flux no measurable intermittency corrections could be found in their scaling laws the seventh order skewness increases by almost two orders of magnitude with respect to the third thus becoming of order unity

non linear dynamics and chaos control for an electromagnetic system a non linear mathematical model has been obtained by applying a modified conventional identification technique based on the principle of harmonic balance in this study analytical work is carried out on this identified non linear model by applying the first harmonic approximation solution and the floquet theory the resulting criteria for bifurcations can be used to evaluate the operational range of a system employing such a non linear actuator we also employ the method of lyapunov exponents to show the occurrence of chaotic motion and to verify the above analyses finally various methods such as the state feedback control and injection of dither signal control are used to control chaos effectively

the inviscid burgers equation with initial data of brownian type the solutions to burgers equation in the limit of vanishing viscosity are investigated when the initial velocity is a brownian motion or fractional brownian motion function i e a gaussian process with scaling exponent 0 h 1 typea or the derivative thereof with scaling exponent 1 h 0 typeb largesize numerical experiments are performed helped by the fact that the solution is essentially obtained by performing a legendre transform the main result is obtained for typea and concerns the lagrangian functionx a which gives the location at timet 1 of the fluid particle which started at the locationa it is found to be a complete devil s staircase the cumulative probability of lagrangian shock intervals a also the distribution of shock amplitudes follows a a h law for small a the remaining regular lagrangian locations form a cantor set of dimensionh in eulerian coordinates the shock locations are everywhere dense the scaling properties of various statistical quantities are also found heuristic interpretations are provided for some of these results rigorous results for the case of brownian motion are established in a companion paper by ya sinai for typeb initial velocities e g white noise there are very few small shocks and shock locations appear to be isolated finally it is shown that there are universality classes of random but smooth non scaling initial velocities such that the long time large scale behavior is after rescaling the same as for typea orb

a novel dynamic framework for subgrid scale parametrization of mesoscale eddies in quasigeostrophic turbulent flows abstract this paper puts forth a modular dynamic subgrid scale modeling framework for large eddy simulation of quasigeostrophic turbulence based on minimizing the errors between structural and functional subgrid scale models the approximate deconvolution ad procedure is used to estimate the free modeling parameters for the eddy viscosity coefficient parameterized in space and time using the smagorinsky and leith models the novel idea here is to estimate the modeling parameters using the ad method rather than the traditionally used test filtering approach first a priori and a posteriori analyses are presented for solving a canonical homogeneous isotropic decaying turbulence problem the proposed model is then applied to a wind driven quasigeostrophic four gyre ocean circulation problem which is a standard prototype of more realistic ocean dynamics results show that the proposed model captures the quasi stationary ocean dynamics and provides the time averaged four gyre circulation patterns taking locally resolved flow characteristics into account the model dynamically provides higher eddy viscosity values for lower resolutions

finite mode analogs of 2d ideal hydrodynamics coadjoint orbits and local canonical structure abstract the algebraic finite mode hydrodynamic type systems that have o n integrals of motion for o n n modes and are intrinsically connected with two dimensional ideal fluid flows are studied special emphasis is given on the structure of their phase space and the problem of finding proper dynamical variables for its description in connection with appropriate problems for the original hydrodynamic equations various possibilities for embedding in the space of canonical variables are demonstrated on the simplest example of the su 3 model giving the finite dimensional analogs of clebsch variables

a fuzzy clustering approach toward hidden markov random field models for enhanced spatially constrained image segmentation hidden markov random field hmrf models have been widely used for image segmentation as they appear naturally in problems where a spatially constrained clustering scheme taking into account the mutual influences of neighboring sites is asked for fuzzy c means fcm clustering has also been successfully applied in several image segmentation applications in this paper we combine the benefits of these two approaches by proposing a novel treatment of hmrf models formulated on the basis of a fuzzy clustering principle we approach the hmrf model treatment problem as an fcm type clustering problem effected by introducing the explicit assumptions of the hmrf model into the fuzzy clustering procedure our approach utilizes a fuzzy objective function regularized by kullback leibler divergence information and is facilitated by application of a mean field like approximation of the mrf prior we experimentally demonstrate the superiority of the proposed approach over competing methodologies considering a series of synthetic and real world image segmentation applications

intermittency in passive scalar decay we consider the decay of a passive scalar in a rough turbulent flow we show that at large times the scalar intensity is statistically equivalent to the product of two independent random variables the first factor is a gaussian variable related to the typical fluctuation at initial conditions the second factor is essentially the probability that in a given realization of the flow tracer particles separate at a very slow rate therefore the large time scalar distribution is always broader than gaussian for any initial condition and large scalar excursions are associated to small relative dispersion events

variational learning for finite dirichlet mixture models and applications in this paper we focus on the variational learning of finite dirichlet mixture models compared to other algorithms that are commonly used for mixture models such as expectation maximization our approach has several advantages first the problem of over fitting is prevented furthermore the complexity of the mixture model i e the number of components can be determined automatically and simultaneously with the parameters estimation as part of the bayesian inference procedure finally since the whole inference process is analytically tractable with closed form solutions it may scale well to large applications both synthetic and real data generated from real life challenging applications namely image databases categorization and anomaly intrusion detection are experimented to verify the effectiveness of the proposed approach

weak solutions of 2 d euler equations with initial vorticity in l log l abstract in this note we prove global in time existence of weak solutions of 2 0 euler equations for incompressible fluid flows in the whole plane of r 2 when the initial vorticity is in the zygmund class l log l the solution is constructed by a vanishing viscosity limit of the sequence of solutions to the navier stokes equations with the same initial data this is a limiting case of the corresponding results of diperna and majda in which global existence of weak solutions was obtained for initial vorticity in l 1 l p 1 p

going forth and back in time a fast and parsimonious algorithm for mixed initial final value problems abstract we present an efficient and parsimonious algorithm to solve mixed initial final value problems the algorithm optimally limits the memory storage and the computational time requirements with respect to a simple forward integration the cost factor is only logarithmic in the number of time steps as an example we discuss the solution of the final value problem for a fokker planck equation whose drift velocity solves a different initial value problem a relevant issue in the context of turbulent scalar transport

numerical simulations of a two layer quasi geostrophic equation of the ocean our object in this article is to present some numerical schemes for a two layer quasi geostrophic model of the ocean and to study the stability of these schemes we prove the unconditional stability of our numerical schemes numerical results from a wind driven two layer quasi geostrophic model of the ocean using these schemes are also presented

on the global regularity of a helical decimated version of the 3d navier stokes equations we study the global regularity for all time and all initial data in h 1 2 o f ar e cently introduced decimated version of the incompressible 3d navier stokes dns equa tions the model is based on a projection of the dynamical evolution of navier stokes ns equations into the subspace where helicity the l 2 scalar product of velocity and vorticity is sign definite the presence of a second beside energy sign definite inviscid conserved quadratic quantity which is equivalent to the h 1 2 sobolev norm allows us to demonstrate global existence and uniqueness of space periodic solutions together with continuity with respect to the initial conditions for this decimated 3d model this is achieved thanks to the establishment of two new estimates for this 3d model which show that the h 1 2 and the time average of the square of the h 3 2 norms of the velocity field remain finite such two additional bounds are known in the spirit of the work of h fujita and t kato arch ration mech anal 16 269 315 1964 rend semin mat univ padova 32 243 260 1962 to be sufficient for showing well posedness for the 3d ns equations furthermore they are di rectly linked to the helicity evolution for the dns model and therefore with a clear physical meaning and consequences

some specific mathematical constraints on 2d turbulence abstract we derive upper and lower bounds for ensemble averages of energy enstrophy and palinstrophy for the 2d periodic navier stokes equations this is carried out both in the general case and in the case where the energy power law for fully developed turbulence holds in the turbulent case the bounds are sharp up to a logarithm and provide a new lower bound on the landau lifschitz degrees of freedom we also prove two properties of the inertial term under the turbulence assumption one is that as the grashof number is increased the ensemble average of this term approaches the force the other is that an estimate of it via the ladyzhenskaya inequality is sharp on a considerable portion of the global attractor

a sufficient condition for the kolmogorov 4 5 law for stationary martingale solutions to the 3d navier stokes equations we prove that statistically stationary martingale solutions of the 3d navier stokes equations on mathbb t 3 subjected to white in time colored in space forcing satisfy the kolmogorov 4 5 law in an averaged sense and over a suitable inertial range using only the assumption that the kinetic energy is o nu 1 as nu rightarrow 0 where is the inverse reynolds number this plays the role of a weak anomalous dissipation no energy balance or additional regularity is assumed aside from that satisfied by all martingale solutions from the energy inequality if the force is statistically homogeneous then any homogeneous martingale solution satisfies the spherically averaged 4 5 law pointwise in space an additional hypothesis of approximate isotropy in the inertial range gives the traditional version of the kolmogorov law we demonstrate a necessary condition by proving that energy balance and an additional quantitative regularity estimate as nu rightarrow 0 imply that the 4 5 law or any similar scaling law cannot hold

a general class of commutative filters for les in complex geometries a class of filters for large eddy simulations of turbulent inhomogeneous flows is presented a general set of rules for constructing discrete filters in complex geometry is given and examples of such filters are presented with these filters the commutation error between numerical differentiation and filtering can be made arbitrarily small allowing for derivation of a consistent set of equations for the large scale field the application of such filters for explicit filtering in large eddy simulations and the issue of boundary conditions for the filtered field are also discussed

a new approach to computing the scaling exponents in fluid turbulence from first principles in this short paper we describe the essential ideas behind a new consistent closure procedure for the calculation of the scaling exponents n of the nth order correlation functions in fully developed hydrodynamic turbulence starting from first principles the closure procedure is constructed to respect the fundamental rescaling symmetry of the euler equation the starting point of the procedure is an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents n this hierarchy was discussed in detail in a recent publication v s l vov and i procaccia physica a 1998 in press chao dyn 9707015 the scaling exponents in this set of equations cannot be found from power counting in this short paper we discuss in detail low order non trivial closures of this infinite set of equations and prove that these closures lead to the determination of the scaling exponents from solvability conditions the equations under consideration after this closure are nonlinear integro differential equations reflecting the nonlinearity of the original navier stokes equations nevertheless they have a very special structure such that the determination of the scaling exponents requires a procedure that is very similar to the solution of linear homogeneous equations in which amplitudes are determined by fitting to the boundary conditions in the space of scales the renormalization scale that is necessary for any anomalous scaling appears at this point the holder inequalities on the scaling exponents select the renormalization scale as the outer scale of turbulence l

count data modeling and classification using finite mixtures of distributions in this paper we consider the problem of constructing accurate and flexible statistical representations for count data which we often confront in many areas such as data mining computer vision and information retrieval in particular we analyze and compare several generative approaches widely used for count data clustering namely multinomial multinomial dirichlet and multinomial generalized dirichlet mixture models moreover we propose a clustering approach via a mixture model based on a composition of the liouville family of distributions from which we select the beta liouville distribution and the multinomial the novel proposed model which we call multinomial beta liouville mixture is optimized by deterministic annealing expectation maximization and minimum description length and strives to achieve a high accuracy of count data clustering and model selection an important feature of the multinomial beta liouville mixture is that it has fewer parameters than the recently proposed multinomial generalized dirichlet mixture the performance evaluation is conducted through a set of extensive empirical experiments which concern text and image texture modeling and classification and shape modeling and highlights the merits of the proposed models and approaches

closure of two dimensional turbulence the role of pressure gradients inverse energy cascade regime of two dimensional turbulence is investigated by means of high resolution numerical simulations numerical computations of conditional averages of transverse pressure gradient increments are found to be compatible with a recently proposed self consistent gaussian model an analogous low order closure model for the longitudinal pressure gradient is proposed and its validity is numerically examined in this case numerical evidence for the presence of higher order terms in the closure is found the fundamental role of conditional statistics between longitudinal and transverse components is highlighted

computing the scaling exponents in fluid turbulence from first principles demonstration of multiscaling we develop a consistent closure procedure for the calculation of the scaling exponents n of the nth order correlation functions in fully developed hydro dynamic turbulence starting from first principles the closure procedure is constructed to respect the fundamental rescaling symmetry of the euler equation the starting point of the procedure is an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents n this hierarchy was discussed in detail in a recent publication by v s l vov and i procaccia the scaling exponents in this set of equations cannot be found from power counting in this paper we present in detail the lowest non trivial closure of this infinite set of equations and prove that this closure leads to the determination of the scaling exponents from solvability conditions the equations under consideration after this closure are nonlinear integro differential equations reflecting the nonlinearity of the original navier stokes equations nevertheless they have a very special structure such that the determination of the scaling exponents requires a procedure that is very similar to the solution of linear homogeneous equations in which amplitudes are determined by fitting to the boundary conditions in the space of scales the renormalization scale that is necessary for any anomalous scaling appears at this point the holder inequalities on the scaling exponents select the renormalization scale as the outer scale of turbulence l we demonstrate that the solvability condition of our equations leads to non kolmogorov values of the scaling exponents n finally we show that this solutions is a first approximation in a systematic series of improving approximations for the calculation of the anomalous exponents in turbulence

diminishing inverse transfer and non cascading dynamics in surface quasi geostrophic turbulence abstract the inverse transfer in the forced dissipative surface quasi geostrophic equation is studied when the natural dissipation operator 1 2 is employed the nonlinear transfer of this system conserves the two quadratic quantities 1 1 4 2 2 and 2 1 2 2 2 kinetic energy where is the stream function and denotes a spatial average in the limit of infinite domain the kinetic energy density 2 remains bounded for the natural dissipation operator for the power law inverse transfer region the inverse flux of 1 diminishes as it proceeds toward sufficiently low wavenumbers whenever the kinetic energy 2 remains bounded this implies that no persistent non dissipative inverse cascade of 1 to ever lower wavenumbers is sustainable as long as the dissipation parameter is held fixed this result does not rule out the possibility that for sufficiently small a finite inverse flux would reach a certain low wavenumber numerical results supporting the theoretical predictions are presented

stochastic models of chaotic systems nonlinear dynamical systems although strictly deterministic often exhibit chaotic behavior which appears to be random the determination of the probabilistic properties of such systems is in general an open problem closure approximations for moment expansion methods have been unsatisfactory more successful has been approximation on the dynamics level by the use of linear stochastic models that attempt to generate the probabilistic properties of the original nonlinear chaotic system as closely as possible examples are reviewed of this approach to simple nonlinear systems to turbulence and to large eddy simulation a stochastic model that simulates the transient energy spectrum of the global atmosphere is developed

intermittency and anomalous scaling of passive scalars in any space dimension we establish exact inequalities for the structure function scaling exponents of a passively advected scalar in both the inertial convective and viscous convective ranges these inequalities involve the scaling exponents of the velocity structure functions and in a refined form an intermittency exponent of the convective range scalar flux they are valid for three dimensional navier stokes turbulence and satisfied within errors by present experimental data the inequalities also hold for any synthetic turbulent velocity statistics with a finite correlation in time we show that for time correlation exponents of the velocity smaller than the local turnover exponent the scalar spectral exponent is strictly less than that in kraichnan s phys rev lett 72 1016 1994 phys fluids 11 945 1968 j fluid mech 64 737 1974 62 305 1974 soluble rapid change model with velocity ensuremath delta correlated in time our results include as a special case an exponent inequality derived previously by constantin and procaccia nonlinearity 7 1045 1994 but with a more direct proof the inequalities in their simplest form follow from a kolmogorov type relation for the turbulent passive scalar valid in each space dimension d our improved inequalities are based upon a rigorous version of the refined similarity hypothesis for passive scalars these are compared with the relations implied by fusion rules hypothesized for scalar gradients textcopyright 1996 the american physical society

explicit filtering and exact reconstruction of the sub filter stresses in large eddy simulation explicit filtering has the effect of reducing numerical or aliasing errors near the grid scale in large eddy simulation les we use a differential filter namely the inverse helmholtz operator which is readily applied to unstructured meshes the filter is invertible which allows the sub filter scale sfs stresses to be exactly reconstructed in terms of the filtered solution unlike eddy viscosity models the method of filtering and reconstruction avoids making any physical assumptions and is therefore valid in any flow regime the sub grid scale sgs stresses are not recoverable by reconstruction but the second order finite element method used here is an adequate source of numerical dissipation in lieu of an sgs model results for incompressible turbulent channel flow at re 180 are presented which show that explicit filtering and exact sfs reconstruction is a significant improvement over the standard les approach of implicit filtering and eddy viscosity sgs modelling

three dimensional forced burgers turbulence supplemented with a continuity equation we investigate turbulent limit of the forced burgers equation supplemented with a continuity equation in three dimensions the scaling exponent of the conditional two point correlation function of density i e r x1 r x2 udu ux12x2u 2a 3 is calculated self consistently in the nonuniversal region from which we obtain a 353 also we derive an equation governing the evolution of the probability density function pdf of longitudinal velocity increments in length scale from which a possible mechanism for the dependence of the inertial pdf to one point urms is developed

a coupled approximate deconvolution and dynamic mixed scale model for large eddy simulation large eddy simulations of incompressible newtonian fluid flows with approximate deconvolution models based on the van cittert method are reported the legendre spectral element method is used for the spatial discretization to solve the filtered navier stokes equations a novel variant of approximate deconvolution models blended with a mixed scale model using a dynamic evaluation of the subgrid viscosity constant is proposed this model is validated by comparing the large eddy simulation with the direct numerical simulation of the flow in a lid driven cubical cavity performed at a reynolds number of 12 000 subgrid modeling in the case of a flow with coexisting laminar transitional and turbulent zones such as the lid driven cubical cavity flow represents a challenging problem moreover the coupling with the spectral element method having very low numerical dissipation and dispersion builds a well suited framework to analyze the efficiency of a subgrid model first and second order statistics obtained using this new model are showing very good agreement with the direct numerical simulation filtering operations rely on an invertible filter applied in a modal basis and preserving the c 0 continuity across elements no clipping on dynamic parameters was needed to preserve numerical stability

parameter estimations of parametrically excited pendulums based on chaos feedback synchronization in this paper an iterate parameter estimation scheme based on chaos feedback synchronization is applied for parametrically excited pendulums the response pendulum can exactly reproduce the system parameters and bifurcation diagram of the drive pendulum thus allowing two chaotic pendulums to be synchronized even though their initial parameter values are quite different the effects of feedback function and feedback weight are investigated feedback and parameter controls suppress the perturbations resulting from noise and parameter mismatches this parameter estimation method based on feedback synchronization is robust to large parameter mismatches