rigorous remarks about scaling laws in turbulent fluids a definition of scaling law for suitable families of measures is given and investigated first a number of necessary conditions are proved they imply the absence of scaling laws for 2d stochastic navier stokes equations and for the stochastic stokes linear problem in any dimension while they imply a lower bound on the mean vortex stretching in 3d second for the 3d stochastic navier stokes equations necessary and sufficient conditions for scaling laws to hold are given translating the problem into bounds for energy and enstrophy of high and low modes respectively unlike in the 2d case the validity or invalidity of such conditions in 3d remains open

gaussian multiplicative chaos for symmetric isotropic matrices motivated by isotropic fully developed turbulence we define a theory of symmetric matrix valued isotropic gaussian multiplicative chaos our construction extends the scalar theory developed by j p kahane in 1985

gaps in the differential forms spectrum on cyclic coverings we are interested in the spectrum of the hodge de rham operator on a mathbb z covering x over a compact manifold m of dimension n 1 let be a hypersurface in m which does not disconnect m and such that m is a fundamental domain of the covering if the cohomology group hn 2 is trivial we can construct for each n in mathbb n a metric g gn on m such that the hodge de rham operator on the covering x g has at least n gaps in its essential spectrum if h n 2 sigma ne 0 the same statement holds true for the hodge de rham operators on p forms provided p notin n 2 n 2 1

twenty five years of multifractals in fully developed turbulence a tribute to giovanni paladin the paper on the multifractal nature of fully developed turbulence and chaotic systems by benzi et al 1984 j phys a math gen 17 3521 has been a starting point of many investigations on the different faces of self similarity and intermittency in turbulent phenomena since then the multifractal model has become a useful tool for the study of small scale turbulence in particular for detailed predictions of different eulerian and lagrangian statistical properties on the occasion of the 50th birthday of our unforgettable friend and colleague giovanni paladin 1958 1996 we review here the basic concepts and some applications of the multifractal model for turbulence

spectral parameter power series for perturbed bessel equations a spectral parameter power series spps representation for regular solutions of singular bessel type sturm liouville equations with complex coefficients is obtained as well as an spps representation for the entire characteristic function of the corresponding spectral problem on a finite interval it is proved that the set of zeros of the characteristic function coincides with the set of all eigenvalues of the sturm liouville problem based on the spps representation a new mapping property of the transmutation operator for the considered perturbed bessel operator is obtained and a new numerical method for solving corresponding spectral problems is developed the range of applicability of the method includes complex coefficients complex spectrum and equations in which the spectral parameter stands at a first order linear differential operator on a set of known test problems we show that the developed numerical method based on the spps representation is highly competitive in comparison to the best available solvers such as sleign2 matslise and some other codes and give an example of an exactly solvable test problem admitting complex eigenvalues to which the mentioned solvers are not applicable meanwhile the spps method delivers excellent numerical results

stochastic interpolation of sparsely sampled time series via multipoint fractional brownian bridges we propose and test a method to interpolate sparsely sampled signals by a stochastic process with a broad range of spatial and or temporal scales to this end we extend the notion of a fractional brownian bridge defined as fractional brownian motion with a given scaling hurst exponent h and with prescribed start and end points to a bridge process with an arbitrary number of intermediate and nonequidistant points determining the optimal value of the hurst exponent h opt appropriate to interpolate the sparse signal is a very important step of our method we demonstrate the validity of our method on a signal from fluid turbulence in a high reynolds number flow and discuss the implications of the non self similar character of the signal the method introduced here could be instrumental in several physical problems including astrophysics particle tracking and specific tailoring of surrogate data as well as in domains of natural and social sciences

kullback leibler divergence measure of intermittency application to turbulence for generic systems exhibiting power law behaviors and hence multiscale dependencies we propose a simple tool to analyze multifractality and intermittency after noticing that these concepts are directly related to the deformation of a probability density function from gaussian at large scales to non gaussian at smaller scales our framework is based on information theory and uses shannon entropy and kullback leibler divergence we provide an extensive application to three dimensional fully developed turbulence seen here as a paradigmatic complex system where intermittency was historically defined and the concepts of scale invariance and multifractality were extensively studied and benchmarked we compute our quantity on experimental eulerian velocity measurements as well as on synthetic processes and phenomenological models of fluid turbulence our approach is very general and does not require any underlying model of the system although it can probe the relevance of such a model

log poisson cascade description of turbulent velocity gradient statistics the log poisson phenomenological description of the turbulent energy cascade is evoked to discuss high order statistics of velocity derivatives and the mapping between their probability distribution functions at different reynolds numbers the striking confirmation of theoretical predictions suggests that numerical solutions of the flow obtained at low moderate reynolds numbers can play an important quantitative role in the analysis of experimental high reynolds number phenomena where small scales fluctuations are in general inaccessible from direct numerical simulations

scale invariance in three dimensional isotropic turbulence a paradox and its resolution if the reynolds number is large enough turbulence is expected to exhibit scale invariance in an intermediate inertial range of wave numbers as shown by power law behaviour of the energy spectrum and also by a constant rate of energy transfer through wave number however although it has long been known that the first of these is true there has been little recognition of the fact that if the second is to hold then there is a contradiction between the definition of the energy flux as the integral of the transfer spectrum and the observed behaviour of the transfer spectrum itself this is because the transfer spectrum t k is invariably found to have a zero crossing at a single point at k0 say implying that the corresponding energy flux cannot have an extended plateau but must instead have a maximum value at k k0 we outline the resulting paradox and note that it may be resolved by the observation that the symmetry of the triadic interactions means that t k is not the relevant transfer term in determining the energy flux instead the relevant term is a filtered partitioned version herein denoted by t k kc where k kc is the cut off wave number for low high pass filtering it is known from studies of spectral subgrid transfer that t k kc is zero over an extended range of wave numbers as this is the case for quite modest reynolds numbers it not only resolves the paradox but may also shed some light on the embarrassment of success of the kolmogorov theory

expansion in series of bessel functions and transmutations for perturbed bessel operators abstract a fitouhi and m m hamza siam j math anal 21 no 6 1990 1619 1632 obtained an expansion in series of bessel functions for eigenfunctions of second order differential operators these series being uniformly convergent on 0 in this paper we give first a new proof of this result leading to a large domain of uniform convergence and then study a transmutation operator between two classes of perturbed bessel operators

the local structure of turbulence in incompressible viscous fluid for very large reynolds numbers 1 we shall denote by u p u x 1 x 2 x 3 t 1 2 3 the components of velocity at the moment t at the point with rectangular cartesian coordinates x 1 x 2 x 3 in considering the turbulence it is natural to assume the components of the velocity u p at every point p x 1 x 2 x 3 t of the considered domain g of the four dimensional space x 1 x 2 x 3 t are random variables in the sense of the theory of probabilities cf for this approach to the problem millionshtchikov 1939 denoting by the mathematical expectation of the random variable a we suppose that 2 and d u d x 2 are finite and bounded in every bounded subdomain of the domain g

dissipative euler flows with onsager critical spatial regularity for any 0 we show the existence of continuous periodic weak solutions v of the euler equations that do not conserve the kinetic energy and belong to the space lt1 cx1 3 e namely x v x t is e holder continuous in space at a e time t and the integral t 1 3 edt is finite a well known open conjecture of l onsager claims that such solutions exist even in the class lt cx1 3 e 2016 wiley periodicals inc

information content of turbulence we treat a turbulent velocity field as a message in the same way as a book or a picture all messages can be described by their entropy per symbol h defined as in shannon s theory of communication in a turbulent flow as the reynolds number re increases more correlated degrees of freedom are excited and participate in the turbulent cascade experiments in a turbulent soap film suggest that the spatial entropy density h is a decreasing function of re namely h proportionality logre const in the logistic map also analyzed here increasing the control parameter r increases h a modified logistic map with additional coupling to past iterations suggests the significance of correlations

collapsing and the differential form laplacian the case of a smooth limit space we analyze the limit of the p form laplacian under a collapse with bounded sectional curvature and bounded diameter to a smooth limit space as an application we characterize when the p form laplacian has small positive eigenvalues in a collapsing sequence

onsager s conjecture almost everywhere in time in recent works by isett holder continuous euler flows in three dimensions with compact support in time pp 1 173 2012 and later by buckmaster et al ann math 2015 iterative schemes were presented for constructing solutions belonging to the holder class c 1 5 e of the 3d incompressible euler equations which do not conserve the total kinetic energy the cited work is partially motivated by a conjecture of lars onsager in 1949 relating to the existence of c 1 3 e solutions to the euler equations which dissipate energy in this note we show how the later scheme can be adapted in order to prove the existence of non trivial holder continuous solutions which for almost every time belong to the critical onsager holder regularity c 1 3 e and have compact temporal support

subensemble decomposition and markov process analysis of burgers turbulence a numerical and statistical study is performed to describe the positive and negative local subgrid energy fluxes in the one dimensional random force driven burgers turbulence burgulence we use a subensemble method to decompose the field into shock wave and rarefaction wave subensembles by group velocity difference we observe that the shock wave subensemble shows a strong intermittency which dominates the whole burgulence field while the rarefaction wave subensemble satisfies the kolmogorov 1941 k41 scaling law we calculate the two subensemble probabilities and find that in the inertial range they maintain scale invariance which is the important feature of turbulence self similarity we reveal that the interconversion of shock and rarefaction waves during the equation s evolution displays in accordance with a markov process which has a stationary transition probability matrix with the elements satisfying universal functions and when the time interval is much greater than the corresponding characteristic value exhibits the scale invariant property

a dyadic model on a tree we study an infinite system of nonlinear differential equations coupled in a tree like structure this system was previously introduced in the literature and it is the model from which the dyadic shell model of turbulence was derived it mimics 3d euler and navier stokes equations in a rough approximation of wavelet decomposition we prove existence of finite energy solutions anomalous dissipation in the inviscid unforced case existence and uniqueness of stationary solutions either conservative or not in the forced case

an efficient numerical verification method for the kolmogorov problem of incompressible viscous fluid some computer assisted proofs of nontrivial steady state solutions for the kolmogorov flows are presented the method is based on the infinite dimensional fixed point theorem using a newton like operator with a numerical verification algorithm that automatically generates a set that includes the exact nontrivial solution when discussing the numerical results we consider the effects of rounding errors in the floating point computations this is a continuation of our study that was presented in watanabe 2009

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

hodge laplace operator on compact manifolds from which a finite number of balls is omitted abstract we study here the convergence of eigenvalues and eigenforms of the laplace operator d d acting on differential forms in the perturbation obtained by omitting a finite number of little balls on a compact riemannian manifold m we restrict ourselves to absolute boundary conditions by duality and show the convergence except at degree dim m 1 where new harmonic forms and one small eigenvalue appear on the perturbed manifold

decaying turbulence in the generalised burgers equation we consider the generalised burgers equation frac partial u partial t f u frac partial u partial x nu frac partial 2 u partial x 2 0 t geqq 0 x in s 1 where f is strongly convex and is small and positive we obtain sharp estimates for sobolev norms of u upper and lower bounds differ only by a multiplicative constant then we obtain sharp estimates for the dissipation length scale and the small scale quantities which characterise the decaying burgers turbulence i e the structure functions and the energy spectrum the proof uses a quantitative version of an argument by aurell et al j fluid mech 238 467 486 1992 note that we are dealing with decaying as opposed to stationary turbulence thus our estimates are not uniform in time however they hold on a time interval t1 t2 where t1 and t2 depend only on f and the initial condition and do not depend on the viscosity these results allow us to obtain a rigorous theory of the one dimensional burgers turbulence in the spirit of kolmogorov s 1941 theory in particular we obtain two results which hold in the inertial range on one hand we explain the bifractal behaviour of the moments of increments or structure functions on the other hand we obtain an energy spectrum of the form k 2 these results remain valid in the inviscid limit

representation of solutions to the one dimensional schrodinger equation in terms of neumann series of bessel functions abstract a new representation of solutions to the equation y q x y 2 y is obtained for every x the solution is represented as a neumann series of bessel functions depending on the spectral parameter due to the fact that the representation is obtained using the corresponding transmutation operator a partial sum of the series approximates the solution uniformly with respect to which makes it especially convenient for the approximate solution of spectral problems the numerical method based on the proposed approach allows one to compute large sets of eigendata with a nondeteriorating accuracy

partial regularity for the stochastic navier stokes equations the effects of random forces on the emergence of singularities in the navier stokes equations are investigated in spite of the presence of white noise the paths of a martingale suitable weak solution have a set of singular points of one dimensional hausdorff measure zero furthermore statistically stationary solutions with finite mean dissipation rate are analysed for these stationary solutions it is proved that at any time t the set of singular points is empty the same result holds true for every martingale solution starting from 0 a e initial condition u 0 where 0 is the law at time zero of a stationary solution finally the previous result is non trivial when the noise is sufficiently non degenerate since for any stationary solution the measure 0 is supported on the whole space h of initial conditions

gabor transform and intermittency in turbulence intermittency effects basically limited to the viscous subrange contaminate the gabor filtering analysis in the inertial subrange the contamination decreases with an increase in the quality factor of the filter and the gabor transform coefficients of turbulent velocity have scaling properties approaching the kolmogorov scaling in the limit of an infinitely long inertial range there is no anomalous scaling i e no non gaussianity the wavelet transform coefficients of turbulent velocity and its structure functions follow probability rules depending on the scales extracted by analyzing wavelet functions this anomalous scaling property is produced by the intermittency effects inherent in the viscous subrange the structure functions cannot extract properties in a pure inertial subrange

partial differential equations with matricial coefficients and generalized translation operators let ao be the bessel operator with matricial coefficients defined on o oo by 4u t u t t2a i u t t where a is a diagonal matrix and let q be an n x n matrix valued function in this work we prove that there exists an isomorphism x on the space of even c cn valued functions which transmutes ao and a q this allows us to define generalized translation operators and to develop harmonic analysis associated with aoa q by use of the riemann method we provide an integral representation and we deduce more precise information on these operators

expansion and asymptotic in terms of basic bessel functions abstract this work aims to study the expansion and asymptotic for solutions of q difference equations in terms of the basic bessel functions namely j 2 x q for this purpose we will show that the constructive method introduced by olver f w j olver asymptotics and special functions academic press inc 1974 and exploited early by fitouhi et al h chebli a fitouhi m m hamza expansion in series of bessel functions and transmutations for perturbed bessel operator j math anal appl 181 3 1994 a fitouhi m m hamza uniform expansion for eigenfunction of singular second order differential operator siam j math anal 21 6 1990 a fitouhi m m hamza expansion in series of laguerre functions for solution of perturbed laguerre equations contemp math 183 1995 a fitouhi j el kamel expansion in series of gegenbauer polynomials int trans sp funct 5 3 4 1997 213 226 can be extended in this context as application new expansions of some basic special functions are established in particular these given by ismail y chen m e h ismail k a muttalib asymptotics of basic bessel functions and q laguerre polynomilas j comput appl math 54 1994 263 272 m e h ismail classical and quantum orthogonal polynomials in one variable cambridge university press 2005

estimates on enstrophy palinstrophy and invariant measures for 2 d turbulence we construct semi integral curves which bound the projection of the global attractor of the 2 d navier stokes equations in the plane spanned by enstrophy and palinstrophy of particular interest are certain regions of the plane where palinstrophy dominates enstrophy previous work shows that if solutions on the global attractor spend a significant amount of time in such a region then there is a cascade of enstrophy to smaller length scales one of the main features of 2 d turbulence theory the semi integral curves divide the plane into regions having limited ranges for the direction of the flow this allows us to estimate the average time it would take for an intermittent solution to burst into a region of large palinstrophy we also derive a sharp universal upper bound on the average palinstrophy and show that it is achieved only for forces that admit statistical steady states where the nonlinear term is zero

collapsing of riemannian manifolds and eigenvalues of laplace operator on etudie la perturbation des valeurs propres de l operateur de laplace sous des deformations des varietes qui ne conservent pas les dimensions

sensitivity analysis on chaotic dynamical systems by non intrusive least squares shadowing nilss abstract this paper develops the non intrusive least squares shadowing nilss method which computes the sensitivity for long time averaged objectives in chaotic dynamical systems in nilss we represent a tangent solution by a linear combination of one inhomogeneous tangent solution and several homogeneous tangent solutions next we solve a least squares problem using this representation thus the resulting solution can be used for computing sensitivities nilss is easy to implement with existing solvers in addition for chaotic systems with many degrees of freedom but few unstable modes nilss has a low computational cost nilss is applied to two chaotic pde systems the lorenz 63 system and a cfd simulation of flow over a backward facing step in both cases the sensitivities computed by nilss reflect the trends in the long time averaged objectives of dynamical systems

scale invariance and the inertial range spectrum in three dimensional stationary isotropic turbulence the assumption of scale invariance when taken in conjunction with the symmetries of the navier stokes equation is shown to lead to the energy spectrum e k e2 3tk 5 3 in the limit of infinite reynolds number here et is the flux of energy due to inertial transfer while the prefactor is determined by an integral over triple correlations of the phases of the system it is argued that this form of the prefactor provides an answer to the landau kraichnan criticism of the original kolmogorov 1941 theory k41

spatiotemporal velocity velocity correlation function in fully developed turbulence turbulence is a ubiquitous phenomenon in natural and industrial flows since the celebrated work of kolmogorov in 1941 understanding the statistical properties of fully developed turbulence has remained a major quest in particular deriving the properties of turbulent flows from a mesoscopic description that is from the navier stokes equation has eluded most theoretical attempts here we provide a theoretical prediction for the functional space and time dependence of the velocity velocity correlation function of homogeneous and isotropic turbulence from the field theory associated to the navier stokes equation with stochastic forcing this prediction which goes beyond kolmogorov theory is the analytical fixed point solution of nonperturbative renormalization group flow equations which are exact in the limit of large wave numbers this solution is compared to two point two times correlation functions computed in direct numerical simulations we obtain a remarkable agreement both in the inertial and in the dissipative ranges

some rigorous results on a stochastic goy model a stochastic infinite dimensional version of the goy model is rigorously investigated well posedness of strong solutions existence and p integrability of invariant measures is proved existence of solutions to the zero viscosity equation is also proved with these preliminary results the asymptotic exponents p of the structure function are investigated necessary and sufficient conditions for 2 2 3 and 2 2 3 are given and discussed on the basis of numerical simulations

the analysis of elliptic families i metrics and connections on determinant bundles in this paper we construct the quillen metric on the determinant bundle associated with a family of elliptic first order differential operators we also introduce a unitary connection on and calculate its curvature our results will be applied to the case of dirac operators in a forthcoming paper

turbulence large scale sweeping and the emergence of small scale kolmogorov spectra the dynamics of fully developed hydrodynamic turbulence still is a basically unsolved theoretical problem due to the strong coupling long range nonlinearities in the navier stokes equations the present analysis focuses on the small scale fluctuations in a turbulent boundary layer with one external length scale yo after taking a 2 1 d spatiotemporal spectral transform of the fluctuating vorticity fields care is taken of large scale sweeping which arises as a collective zero mode from the nonlinear flow terms the unswept small scale nonlinearities are then shown to be asymptotically locally isotropic i e for wave numbers k by internal consistency which allows to close the nonlinear hierarchy the navier stokes equations without external forcing are integrated to give the spectral response of the fluctuating small scale velocity fields on the presence of a locally isotropic blob of turbulence while it is being swept around over an arbitrary steady state mean velocity profile using viscous boundary conditions at y 0 averaging the response spectrum over all possible orientational configurations and sweep velocities results in a novel self consistency integral for the 4d energy spectrum function the distribution of turbulence sweep velocities is modeled by means of levy type densities having an algebraic tail with power p 1 the generic case which includes von karman s logarithmic mean velocity profile is found to correspond to 1 p 3 asymptotic analysis of the self consistency integral leads to a differential equation which fixes the scaling exponent of the unswept frequency and admits a nonempty integrable and positive definite airy type frequency spectrum ei k k k with so called normal kolmogorov scaling that is 7 3 and 2 3 anomalous scaling is possible for one special mean profile

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

direct dynamical energy cascade in the modified kdv equation in this study we examine the energy transfer mechanism during the nonlinear stage of the modulational instability mi in the modified korteweg de vries equation the particularity of this study consists in considering the problem essentially in the fourier space a dynamical energy cascade model of this process originally proposed for the focusing nls type equations is transposed to the mkdv setting using the existing connections between the kdv type and nls type equations the main predictions of the d cascade model are outlined and thoroughly discussed finally the obtained theoretical results are validated by direct numerical simulations of the mkdv equation using the pseudo spectral methods a general good agreement is reported in this study the nonlinear stages of the mi evolution are also investigated for the mkdv equation

predicting foreign currency exchange rates using the numerical solution of the incompressible navier stokes equations abstract the movement of exchange rates has similarities with physical phenomena especially the movement of fluid in turbulence the parameters change of the data information on the foreign exchange market will result in unstable exchange rates movement these are according to changes in energy in the turbulence flow resulting in fluid particles moving randomly at fluctuating velocity this study will predict the exchange rates of the united states dollar usd to indonesian rupiah idr using the incompressible navier stokes equations which have been modified with economic parameters the analogy of economic parameters to physical parameters such as gross domestic product gdp as the distance between the two measured velocity points the trade balance of two countries as fluid viscosity and fluid flow velocity as exchange rate changes while the inflation rates and interest rates are external forces the numerical solution of the navier stokes equations is solved using the crank nicolson finite difference method the results of the prediction of the exchange rate of usd to idr are compared with actual exchange rate data the exchange rate prediction results of the navier stokes equations that calculated using the crank nicolson scheme for one year produce an error percentage below 2 5 of the actual exchange rate data

sensitivity analysis on chaotic dynamical systems by finite difference non intrusive least squares shadowing fd nilss abstract we present the finite difference non intrusive least squares shadowing fd nilss algorithm for computing sensitivities of long time averaged quantities in chaotic dynamical systems fd nilss does not require tangent solvers and can be implemented with little modification to existing numerical simulation software we also give a formula for solving the least squares problem in fd nilss which can be applied in nilss as well finally we apply fd nilss for sensitivity analysis of a chaotic flow over a 3 d cylinder at reynolds number 525 where fd nilss computes accurate sensitivities and the computational cost is in the same order as the numerical simulation

magnetohydrodynamic turbulent flows existence results abstract in this paper we provide a detailed investigation of the problem of existence of solutions to the stochastic magnetohydrodynamic equations which describe the motion of turbulent particles of fluids in a magnetic field the results are proved through a delicate combination of galerkin approximation scheme with some deep compactness results of analytic and probabilistic nature

highly turbulent solutions of the lagrangian averaged navier stokes alpha model and their large eddy simulation potential we compute solutions of the lagrangian averaged navier stokes alpha lans alpha model for significantly higher reynolds numbers up to re approximately 8300 than have previously been accomplished this allows sufficient separation of scales to observe a navier stokes inertial range followed by a second inertial range specific to the lans alpha model both fully helical and nonhelical flows are examined up to reynolds numbers of approximately 1300 analysis of the third order structure function scaling supports the predicted l3 scaling it corresponds to a k 1 scaling of the energy spectrum for scales smaller than alpha the energy spectrum itself shows a different scaling which goes as k1 this latter spectrum is consistent with the absence of stretching in the subfilter scales due to the taylor frozen in hypothesis employed as a closure in the derivation of the lans alpha model these two scalings are conjectured to coexist in different spatial portions of the flow the l3 e k approximately k 1 scaling is subdominant to k1 in the energy spectrum but the l3 scaling is responsible for the direct energy cascade as no cascade can result from motions with no internal degrees of freedom we demonstrate verification of the prediction for the size of the lans alpha attractor resulting from this scaling from this we give a methodology either for arriving at grid independent solutions for the lans alpha model or for obtaining a formulation of the large eddy simulation optimal in the context of the alpha models the fully converged grid independent lans alpha model may not be the best approximation to a direct numerical simulation of the navier stokes equations since the minimum error is a balance between truncation errors and the approximation error due to using the lans alpha instead of the primitive equations furthermore the small scale behavior of the lans alpha model contributes to a reduction of flux at constant energy leading to a shallower energy spectrum for large alpha these small scale features however do not preclude the lans alpha model from reproducing correctly the intermittency properties of the high reynolds number flow

a local two radii theorem on the chebli trimeche hypergroup let 0 r1 r2 r1 r2 r it is given a necessary and sufficient condition so that the null function is the unique solution f c r r of the system 1 0 ritxf y a y dy 0 x r ri i 1 2 where a y dy is the haar measure and tx is the x translation operator on the chebli trimeche hypergroup the result obtained is especially available for bessel kingmann and jacobi hypergroups

multifractal asymptotic modeling of the probability density function of velocity increments in turbulence moments and probability density functions pdf of absolute value velocity increments jv xc v x j in turbulence are linked by simple integral relations it is shown that the steepest descent method can be applied to evaluate the integrals if the moments the absolute value structure functions obey multifractal scaling laws of the type hjv x c v x j n id an n a double asymptotic relation then relates the moments to the pdf the dominant exponential terms of the asymptotic relation naturally yield the legendre transform that is at the core of the parisi frisch model of inertial range intermittency using the asymptotic relation the pdf can be reconstructed from the multifractal exponent spectrum n and the statistics of large scale moments on the basis of experimental results it is shown that moments are quantitatively represented by multifractal scaling laws and large scale gaussian or quasi gaussian statistics the large scale at which the statistics are gaussian or quasi gaussian is determined from inertial range data alone and is of the order of the integral scale for taylor scale reynolds numbers r in the range 300 2200 this representation of moments together with the double asymptotic relations is able to reconstruct quantitatively the experimental inertial range pdf analytic expressions she leveque and log normal of scaling exponents are both shown to lead to reconstructed pdf with systematic deviations from experiment 1999 published by elsevier science b v all rights reserved

anomalous dissipation for 1 5 holder euler flows recently the second and fourth authors developed an iterative scheme for obtaining rough solutions of the 3d incompressible euler equations in holder spaces the motivation comes from onsager s conjecture the construction involves a superposition of weakly interacting perturbed beltrami flows on infinitely many scales an obstruction to better regularity arises from the errors in the linear transport of a fast periodic flow by a slow velocity field in a recent paper the third author has improved upon the methods introducing some novel ideas on how to deal with this obstruction thereby reaching a better holder exponent albeit weaker than the one conjectured by onsager in this paper we give a shorter proof of this final result adhering more to the original scheme of the second and fourth authors and introducing some new devices more precisely we show that for any positive e there exist periodic solutions of the 3d incompressible euler equations that dissipate the total kinetic energy and belong to the holder class c 1 5 epsilon

on the asymptotic behavior of average energy and enstrophy in 3d turbulent flows abstract rigorous upper and lower bounds are proved for the taylor and the kolmogorov wavenumbers for the three dimensional space periodic navier stokes equations under the assumption that kolmogorov s two thirds power law holds the bounds sharpen to t gr 1 4 and gr 3 8 respectively where gr is the grashof number this provides a rigorous proof that the power law implies 1 the energy cascade 2 kolmogorov dissipation law and 3 a connection between t and the portion of phase space where a key a priori estimate on the nonlinear term is sharp is shown to be significant by means of a lower bound on any probability measure associated with an infinite time average

transformation operators for spherical schrodinger operators abstract the present work aims at obtaining estimates for transformation operators for one dimensional perturbed radial schrodinger operators it provides more details and suitable extensions to already existing results that are needed in other recent contributions dealing with these kinds of operators

dynamical origins for non gaussian vorticity distributions in turbulent flows we present results on the connection between the vorticity equation and the shape and evolution of the single point vorticity probability density function the statistical framework for these observations is based on the classical hierarchy of evolution equations for the probability density functions by lundgren novikov and monin combined with conditional averaging of the unclosed terms the numerical evaluation of these conditional averages provides insights into the intimate relation of dynamical effects such as vortex stretching and vorticity diffusion and non gaussian vorticity statistics