wall pressure and shear stress spectra from direct simulations of channel flow wall pressure and shear stress spectra from direct numerical simulations of turbulent plane channel flow are presented in this paper simulations have been carried out at a series of reynolds numbers up to re 1440 which corresponds to re 6 92 x 10 4 based on channel width and centerline velocity single point and two point statistics for velocity pressure and their derivatives have been collected including velocity moments up to fourth order the results have been used to study the reynolds number dependence of wall pressure and shear stress spectra it is found that the point spectrum of wall pressure collapses for re 360 under a mixed scaling for frequencies lower than the peak frequency of the frequency weighted spectrum and under viscous scaling for frequencies higher than the peak point spectra of wall shear stress components are found to collapse for re 360 under viscous scaling the normalized mean square wall pressure increases linearly with the logarithm of reynolds number the rms wall shear stresses also increase with reynolds number over the present range but suggest some leveling off at high reynolds number

finite surface discretization for incompressible navier stokes equations and coupled conservation laws abstract we present a new finite surface discretization fsd aiming at the incompressible navier stokes equations nse and other coupled conservation laws this discretization defines the velocities as surfaced averaged values living on the faces of the pressure volumes in which the mass is set to be conserved consequently the calculation of the mass balance on these control volumes is exact which allows more accurate information to be kept in the velocity field and produces a very accurate prediction of the pressure in the next time step the proposed discretization reduces the stencil size of the poisson equation in the projection method compared to the finite volume and finite difference discretizations due to highly accurate mass conservation the compact sixth order approximation of fsd can be used with an explicit fourth order pressure treatment this property greatly reduces the cost and complexity of the implementation we present the discrete evolution equation of the surface averaged velocities together with the enforcement of mass conservation and the solution procedure for the pressure the approximation of the nse under this new discretization uses a combination of finite difference and finite volume methods the proposed method is validated using standard laminar test cases we identify the conditions under which a fourth order pressure treatment can support the sixth order and eighth order approximations of the convection term using fourier analysis the performance of the method is evaluated on turbulent channel flows up to friction reynolds number of 950 the quantitative relationships between the accuracy of the solution and grid size are identified we present two performance indices for comparison with other methods at the error level of 1 per mille the proposed method is 28 times faster than the classic second order scheme

recursive two way parabolic equation approach for modeling terrain effects in tropospheric propagation the fourier split step method is a one way marching type algorithm to efficiently solve the parabolic equation for modeling electromagnetic propagation in troposphere the main drawback of this method is that it characterizes only forward propagating waves and neglects backward propagating waves which become important especially in the presence of irregular surfaces although ground reflecting boundaries are inherently incorporated into the split step algorithm irregular surfaces such as sharp edges introduce a formidable challenge in this paper a recursive two way split step algorithm is presented to model both forward and backward propagation in the presence of multiple knife edges the algorithm starts marching in the forward direction until the wave reaches a knife edge the wave arriving at the knife edge is partially reflected by imposing the boundary conditions at the edge and is propagated in the backward direction by reversing the paraxial direction in the parabolic equation in other words the wave is split into two components and the components travel in their corresponding directions the reflected wave is added to the forward wave in each range step to obtain the total wave the wave splitting is performed each time a wave is incident on one of the knife edges this procedure is repeated until convergence is achieved inside the entire domain

a third order multistep time discretization for a chebyshev tau spectral method a time discretization scheme based on the third order backward difference formula has been embedded into a chebyshev tau spectral method for the navier stokes equations the time discretization is a variant of the second order backward scheme proposed by krasnov et al 2008 3 high resolution direct numerical simulations of turbulent incompressible channel flow have been performed to compare the backward scheme to the runge kutta scheme proposed by spalart et al 1991 2 it is shown that the runge kutta scheme leads to a poor convergence of some third order spatial derivatives in the direct vicinity of the wall derivatives that represent the diffusion of wall tangential vorticity the convergence at the wall is shown to be significantly improved if the backward scheme is applied

evidence of nonlogarithmic behavior of turbulent channel and pipe flow employing data of peak position and peak values of reynolds shear stress provided by canonical channel flow direct numerical simulations and pipe and channel flow experiments three recent theories predicting the mean velocity profile of wall bounded turbulent flows are compared based on that analysis it is verified that the mean velocity profile of such internal flows is logarithmic only to leading order and that the higher order terms are proportional to reciprocal powers of the karman number this finding clearly indicates that higher order effects with respect to the karman number and the wall normal coordinate must be considered furthermore our results show that even the statistics of the flow region closest to the wall are affected by flow phenomena that scale with outer variables

the character of the turbulent wall pressure spectrum at subconvective wavenumbers and a suggested comprehensive model the likely character of the wavevector frequency spectrum of turbulent wall pressure on a smooth rigid plane is reexamined also modeling is extended for low mach numbers to the acoustic wavenumber domain from the relation of the wavevector frequency amplitude of wall pressure to amplitudes of fluctuating vorticity related velocity products reynolds stresses regarded as its sources the dependence of the wall pressure spectrum at subconvective wavenumbers is seen to depend essentially on the rate of decrease of the source cross spectra with wall distance y and on the identity of the wavenumber coefficient e g v or 1 that scales this profile a model wall pressure spectrum proposed earlier is generalized with respect to this rate of decrease and found to permit a range of possible dependences between k0 and k2 in that part of the subconvective domain where k 1 if a contribution to the source spectrum exists that is roughly independent of wall distance for v y k 1 it may dominate the wall pressure in the subconvective range and lead for k 1 to wavenumber independence of the spectrum in accord with the martin leehey wind tunnel measurement a comprehensive trial model for the wall pressure spectrum based on source models yielding this character is proposed and viewed as potentially satisfactory in all wavenumber domains from the acoustic to the convective for c k 1 it varies as k2 as follows for any source spectral profile that decreases at least as y 4 for y and accords with the phillips kraichnan theorem

an efficient approximation for the vibro acoustic response of a turbulent boundary layer excited panel the aim of this study was to present a deterministic model for approximating the vibrations and the acoustic pressure radiated when a thin elastic plate is immersed in a low mach number flow of fluid as a prelude to this study a classical random model based on a wavevector integration technique was used in the case of a low mach number turbulent flow the numerical study showed that the subconvective region of the turbulent excitation power spectrum contributes significantly to the response of the panel a deterministic approximate model was developed based on this behaviour of the system

probability distribution functions and coherent structures in a turbulent channel with the aid of a direct numerical simulation of an incompressible plane turbulent channel at h 162 we have determined the probability distribution functions pdf s of pressure and of the various velocity components from the wall to the channel center the pressure turns out to be symmetric with exponential tails at the wall as well as at y 2 5 at y 12 where the streamwise streaks intensity is maximum the pressure has become asymmetric this character intensifies with the distance away from the wall and the distribution obtained in the channel center resembles those determined in isotropic turbulence and free shear flows very close to the wall y 2 5 the pdf of u ensuremath is highly skewed with exponential and sub gaussian distributions at high and low values respectively this indicates that the high speed streaks are very intermittent at the wall the reverse occurs close to the channel center where intense negative u ensuremath prevail then we show that the most probable orientation of the fluctuating vorticity vector is perpendicular to the wall in the region 5l y l30 which is basically in the low and high speed regions while it is 45 ifmmode circ else textdegree fi with respect to the wall above

propagation modeling over irregular terrain by the improved two way parabolic equation method the two way split step parabolic equation 2w sspe method is improved to be able to model both forward and backward waves propagation over irregular perfectly electrical conducting pec surfaces and irregular lossy surfaces with impedance boundary conditions ibc the discrete mixed fourier transform dmft is applied in both forward and backward direction to deal with ibc and the boundary shift bs method is used to dispose of the irregular terrain effects numerical results obtained by the improved 2w sspe algorithm for several typical scenarios with different ground types are compared with those got by the previous 2w sspe method and the one way parabolic equation method

reply to comments on propagation modeling over irregular terrain by the improved two way parabolic equation method in this paper we focused on deriving and refining the two way parabolic equation 2wpe formulations and developing the improved two way split step parabolic equation 2w sspe method to model both forward and backward propagating waves over various lossy surfaces with impedance boundary conditions ibc in urban and tropospheric scenarios

extraction of the acoustic component of a turbulent flow exciting a plate by inverting the vibration problem abstract an improvement of the force analysis technique fat an inverse method of vibration is proposed to identify the low wavenumbers including the acoustic component of a turbulent flow that excites a plate this method is a significant progress since the usual techniques of measurements with flush mounted sensors are not able to separate the acoustic and the aerodynamic energies of the excitation because the aerodynamic component is too high moreover the main cause of vibration or acoustic radiation of the structure might be due to the acoustic part by a phenomenon of spatial coincidence between the acoustic wavelengths and those of the plate this underlines the need to extract the acoustic part in this work numerical experiments are performed to solve both the direct and inverse problems of vibration the excitation is a turbulent boundary layer and combines the pressure field of the corcos model and a diffuse acoustic field these pressures are obtained by a synthesis method based on the cholesky decomposition of the cross spectra matrices and are used to excite a plate thus the application of the inverse problem fat that requires only the vibration data shows that the method is able to identify and to isolate the acoustic part of the excitation indeed the discretization of the inverse operator motion equation of the plate acts as a low pass wavenumber filter in addition this method is simple to implement because it can be applied locally no need to know the boundary conditions and measurements can be carried out on the opposite side of the plate without affecting the flow finally an improvement of fat is proposed it regularizes optimally and automatically the inverse problem by analyzing the mean quadratic pressure of the reconstructed force distribution this optimized fat in the case of the turbulent flow has the advantage of measuring the acoustic component up to higher frequencies even in the presence of noise

semi implicit runge kutta schemes development and application to compressible channel flow time stepconstraintdueto thefine meshnear thewall the explicitsubschemeis asix stage fourth order low storage runge kutta scheme based on analysis in fourier space and results obtained for propagation test cases the semiimplicitschemesareshowntobeoforder3and forwavesdiscretizedbyanumberofpointsperperiodbetween4and 16 tobeasaccurateas ormoreaccuratethan thestandardexplicitfourth orderrunge kuttaalgorithmintermsof dissipationanddispersion thelarge eddysimulationofacompressibleturbulentchannelflowatafrictionreynolds numberof360andamachnumberof0 1isthencarriedoutwithoneoftheproposedalgorithms thecomputational time is reduced by a factor 1 33 with respect to a large eddy simulation using the explicit subscheme in all directions wall pressure and velocity spectra from the large eddy simulation are presented to give insights into the flow turbulent structures in particular wave number frequency spectra are calculated acoustic components appear to be identified in these spectra

modal forcing functions for structural vibration from turbulent boundary layer flow abstract in this paper several approaches for combining large scale finite element structural vibration models with turbulent boundary layer tbl forcing functions are evaluated the objective is to determine an efficient method to predict the surface displacement and radiated acoustic power the overall formulation is based on a standard modal summation approach and the focus of this work is the calculation of the modal force matrix direct numerical integration of the modal force is shown to be very computationally intensive and requires overly resolved structural models however an asymptotic approximation to the tbl model provides a very efficient method to compute the modal force at high frequencies the asymptotic results are equivalent to full numerical integration when the tbl correlation lengths are roughly an order of magnitude smaller than the structural wavelengths additionally the asymptotic solution also removes any dependence of the structural mesh resolution analytical formulas using this approach are derived for structures with and without free edges example results are shown for a simple isotropic plate and for a complex rib stiffened plate at low speed in water

weil restriction of noncommutative motives abstract the weil restriction functor introduced in the late fifties was recently extended by karpenko to the category of chow motives with integer coefficients in this article we introduce the noncommutative nc analogue of the weil restriction functor where schemes are replaced by dg algebras and extend it to kontsevich s categories of nc chow motives and nc numerical motives instead of integer coefficients we work more generally with coefficients in a binomial ring along the way we extend karpenko s functor to the classical category of numerical motives and compare this extension with its nc analogue as an application we compute the nc chow motive of the weil restriction of every smooth projective scheme whose category of perfect complexes admits a full exceptional collection finally in the case of central simple algebras we describe explicitly the nc analogue of the weil restriction functor using solely the degree of the field extension this leads to a categorification of the classical corestriction homomorphism between brauer groups

surface pressure fluctuations beneath two and three dimensional turbulent boundary layers surface pressure fluctuation measurements were made in two dimensional turbulent boundary layers at two reynolds numbers re 7 3 10 3 and 2 34 104 and pressure driven three dimensional turbulent boundary layers at two reynolds numbers approach re 5 94 x 10 3 and 2 32 104 the collapse of spectral levels at middle and high frequencies and the effects of inner and outer boundary layer scaling variables are shown for a wide range of reynolds numbers 1 4 x 10 3 2 34 104 for the two dimensional flows such scaling parameters do not collapse the pressure spectra beneath three dimensional flows which have a nearly constant or flat midfrequency range and at some measurement stations and spectral levels within the flat and high frequency spectral ranges that significantly raise p additionally dimensional spectral levels within the flat frequency range are independent of reynolds number analysis based on the poisson equation shows that the variation of the high frequency spectral levels is related to the variation in near wall mean velocity gradients and 2 structure due to the spanwise pressure gradient

compact fourth order finite volume method for numerical solutions of navier stokes equations on staggered grids the development of a compact fourth order finite volume method for solutions of the navier stokes equations on staggered grids is presented a special attention is given to the conservation laws on momentum control volumes a higher order divergence free interpolation for convective velocities is developed which ensures a perfect conservation of mass and momentum on momentum control volumes three forms of the nonlinear correction for staggered grids are proposed and studied the accuracy of each approximation is assessed comparatively in fourier space the importance of higher order approximations of pressure is discussed and numerically demonstrated fourth order accuracy of the complete scheme is illustrated by the doubly periodic shear layer and the instability of plane channel flow the efficiency of the scheme is demonstrated by a grid dependency study of turbulent channel flows by means of direct numerical simulations the proposed scheme is highly accurate and efficient at the same level of accuracy the fourth order scheme can be ten times faster than the second order counterpart this gain in efficiency can be spent on a higher resolution for more accurate solutions at a lower cost

vibroacoustic response of a thin cylindrical shell excited by a turbulent internal flow comparison between numerical prediction and experimentation the main aspect of this work is to establish a comparison between the measured and the modelled vibroacoustic response of a thin cylindrical pipe excited by a turbulent internal flow the first part presents the experiment a corcos like model of the wall pressure fluctuation is proposed the vibroacoustic response of the shell is measured a numerical method based on a boundary integral formulation and a matched asymptotic expansion is developed computed spectral densities of the velocity of and acoustic sound pressure radiated by the shell are compared with experimental results the comparison shows an agreement within a few decibels

derived categories of keum s fake projective planes abstract we conjecture that derived categories of coherent sheaves on fake projective n spaces have a semi orthogonal decomposition into a collection of n 1 exceptional objects and a category with vanishing hochschild homology we prove this for fake projective planes with non abelian automorphism group such as keum s surface then by passing to equivariant categories we construct new examples of phantom categories with both hochschild homology and grothendieck group vanishing

kuchle fivefolds of type c5 we show that kuchle fivefolds of type c5 subvarieties of the grassmannian mathrm mathsf gr 3 7 parameterizing 3 subspaces that are isotropic for a given 2 form and are annihilated by a given 4 form are birational to hyperplane sections of the lagrangian grassmannian mathrm mathsf sgr 3 6 and describe in detail these birational transformations as an application we show that the integral chow motive of a kuchle fivefold of type c5 is of lefschetz type we also discuss kuchle fourfolds of type c5 hyperplane sections of the corresponding kuchle fivefolds an interesting class of fano fourfolds which is expected to be similar to the class of cubic fourfolds in many aspects

from exceptional collections to motivic decompositions via noncommutative motives making use of noncommutative motives we relate exceptional collections and more generally semi orthogonal decompositions to motivic decompositions on one hand we prove that the chow motive m x q of every smooth and proper deligne mumford stack x whose bounded derived category d b x of coherent schemes admits a full exceptional collection decomposes into a direct sum of tensor powers of the lefschetz motive examples include projective spaces quadrics toric varieties homogeneous spaces fano threefolds and moduli spaces on the other hand we prove that if m x q decomposes into a direct sum of tensor powers of the lefschetz motive and moreover d b x admits a semiorthogonal decomposition then the noncommutative motive of each one of the pieces of the semi orthogonal decomposition is a direct sum of units as an application we obtain a simplification of dubrovin s conjecture

the projection method for the incompressible navier stokes equations the pressure near a no slip wall an explicit staggered projection method for the incompressible navier stokes equations with no slip walls is analyzed and used in simulations to address several issues related to the pressure boundary condition required when the continuity equation is replaced by the standard pressure poisson equation ppe 2 p u u f first it is shown that a ppe system supplemented with a neumann pressure boundary condition derived from the momentum equation can be made consistent with the navier stokes equations if it is extended with the requirement that 2 u 0 is zero near the wall and the solution is sufficiently smooth this implies that it is possible to formulate a boundary condition for the standard ppe without the necessity to resort to green s functions which is interesting for theoretical reasons second the equivalence is shown between the staggered projection method and the staggered discretization of above ppe system the derivation of the equivalence sheds light upon the so called ppe paradox and leads to an approximation of the wall value of p n which is not required but implied by the staggered projection method third the near wall regularity of a solution of the navier stokes equations is numerically analyzed by means of direct numerical simulation of turbulent channel flow performed with the staggered projection method from the numerical inspection of all terms of the momentum equation in the near wall region it is concluded that the three components of the momentum equation are satisfied on the wall for t 0 for short times but also in the turbulent regime in the limit t 0 the pressure gradient is observed to converge to the initial pressure gradient in the l 2 norm which confirms a disputed theoretical result in literature even in the maximum norm the pressure gradient appears to converge to the initial pressure gradient the only discontinuities observed in the simulations are the discontinuities of the tangential viscous terms and the time derivatives of the tangential velocities on the wall at t 0 thus the numerical results indicate that the regularity of the solution for turbulent channel flow is stronger than claimed by existing theory