High-resolution Direct Numerical Simulations Research Articles

Statistics of Energy Transfer in High-Resolution Direct Numerical Simulation of Turbulence in a Periodic Box

The statistics of energy transfer is studied by using the data of a series of high-resolution direct numerical simulations of incompressible homogeneous turbulence in a periodic box with the Taylor micro-scale Reynolds number R λ and grid points up to approximately 1130 and 4096 3 , respectively. The data show that the energy transfer T across the wave number k is highly intermittent and the skewness S and flatness F of T increase with k approximately as S ∝( k L ) α S , F ∝( k L ) α F in the inertial subrange, where α S ∼2/3, α F ∼1 and L the characteristic length scale of energy containing eddies. The comparison between the statistics of T , the energy dissipation rate e and its average e r over a domain of scale r shows that T is less intermittent than e, while there is a certain similarity between the probability distribution functions of T and e r .

Multiparticle dispersion in fully developed turbulence

The statistical geometry of dispersing Lagrangian clusters of four particles (tetrahedra) is studied by means of high-resolution direct numerical simulations of three-dimensional homogeneous isotropic turbulence. We give evidence of a self-similar regime of shape dynamics characterized by almost two-dimensional, strongly elongated geometries. The analysis of four-point velocity-difference statistics and orientation shows that inertial-range eddies typically generate a straining field with a strong extensional component aligned with the elongation direction and weak extensional/compressional components in the orthogonal plane.

Large eddy simulations of two-dimensional turbulent convection in a density-stratified fluid

Large eddy simulations (LES) of two-dimensional turbulent convection within the anelastic approximation are presented for Rayleigh number Ra = 109, Prandtl number Pr = 1 with free-slip boundary conditions. Various subgrid-scale (SGS) models are investigated such as a similarity model, a dynamic similarity model, a dynamic eddy-viscosity model, a hyperdiffusion model and a hybrid model (dynamic similarity hyperdiffusion model). To study the effects of density stratification on the models, we have also carried out simulations for a Boussinesq flow. The SGS models are compared to direct numerical simulation (DNS) data on the basis of kinetic energy and entropy variance spectra, mean entropy profiles, r.m.s. entropy profiles and r.m.s. kinetic energy density profiles. The results show that for the Boussinesq flow, all the SGS models agree fairly well with the high resolution DNS data. However, for the strongly density-stratified flow, only the hyperdiffusion and the hybrid model show good performance.

Optimal solenoidal interpolation of turbulent vector fields: application to PTV and super-resolution PIV

A new approach for the interpolation of a filtered turbulence velocity field given random point samples of unfiltered turbulence velocity data is described. In this optimal interpolation method, the best possible value of the interpolated filtered field is obtained as a stochastic estimate of a conditional average, which minimizes the mean square error between the interpolated filtered velocity field and the true filtered velocity field. Besides its origins in approximation theory, the optimal interpolation method also has other advantages over more commonly used ad hoc interpolation methods (like the ‘adaptive Gaussian window’). The optimal estimate of the filtered velocity field can be guaranteed to preserve the solenoidal nature of the filtered velocity field and also the underlying correlation structure of both the filtered and the unfiltered velocity fields. The a posteriori performance of the optimal interpolation method is evaluated using data obtained from high-resolution direct numerical simulation of isotropic turbulence. Our results show that for a given sample data density, there exists an optimal choice of the characteristic width of cut-off filter that gives the least possible relative mean square error between the true filtered velocity and the interpolated filtered velocity. The width of this ‘optimal’ filter and the corresponding minimum relative error appear to decrease with increase in sample data density. Errors due to the optimal interpolation method are observed to be quite low for appropriate choices of the data density and the characteristic width of the filter. The optimal interpolation method is also seen to outperform the ‘adaptive Gaussian window’, in representing the interpolated field given the data at random sample locations. The overall a posteriori performance of the optimal interpolation method was found to be quite good and hence makes a potential candidate for use in interpolation of PTV and super-resolution PIV data.

Energy Spectrum in the Near Dissipation Range of High Resolution Direct Numerical Simulation of Turbulence

The energy spectrum in the near dissipation range of turbulence is studied by analyzing the data of a series of high-resolution direct numerical simulations of incompressible homogeneous turbulence...

Energy fluxes and shell-to-shell transfers in three-dimensional decaying magnetohydrodynamic turbulence

A spectral analysis of the energy cascade in magnetohydrodynamics (MHD) is presented using high-resolution direct numerical simulation of decaying isotropic turbulence. The Fourier representations of both the velocity and the magnetic fields are split into subsets that correspond to shells of wave vectors. A detailed study of the shell-to-shell interactions is performed and a comparison with theoretical prediction based on field-theoretic method is proposed. Two different definitions for the forward and backward energy transfers are suggested. They provide diagnostics that can be used in order to assess subgrid-scale modeling in large eddy simulation for turbulent MHD systems.

Particle trapping in three-dimensional fully developed turbulence

The statistical properties of fluid particles transported by a three-dimensional fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. Single trajectory statistics are investigated in a time range spanning more than three decades, from less than a tenth of the Kolmogorov time scale, τη, up to one large-eddy turnover time. Our analysis reveals the existence of relatively rare trapping events in vortex filaments which give rise to enhanced intermittency on Lagrangian observables up to 10τη. Lagrangian velocity structure function attain scaling properties in agreement with the multifractal prediction only for time lags larger than those affected by trapping.

The residual energy in freely decaying magnetohydrodynamic turbulence

Within the framework of the eddy-damped quasi-normal Markovian approximation for incompressible isotropic magnetohydrodynamic (MHD) turbulence a prediction for the inertial range scaling of the residual energy spectrum, , is obtained. This scaling, while in contradiction to earlier theoretical results, is shown to be in agreement with high-resolution direct numerical simulations of nonhelical decaying MHD turbulence. The underlying phenomenology states a dynamic quasi-equilibrium of the small-scale turbulent dynamo and the Alfvén effect.

Direct numerical simulation and large-eddy simulation of a shear-free mixing layer

High resolution direct numerical simulation (DNS) (512×1024×512) and large-eddy simulation (LES) of a shear-free mixing layer are presented. The geometry of the flow consists of two layers with different turbulence intensities that are in contact and interact through a fairly thin mixing layer. This geometry is used to explore the influence of inhomogeneities in the characteristic length scales, times scales and energy scales on the turbulence properties. Comparison of DNS results is made with the Veeravalli & Warhaft (J. Fluid Mech.207, 191–229, 1989) experiment. The LES is performed on a 32×64×32 grid using an eddy-viscosity model. The use of such a model appears to be justified by the very weak departures from isotropy that are observed in the shear-free mixing layer. The LES predictions are compared with the filtered DNS data and show that the eddy viscosity model performs very well in predicting the energy profile as well as the deviation from Gaussianity in the turbulent velocity field statistics.

Multifractal statistics of Lagrangian velocity and acceleration in turbulence.

The statistical properties of velocity and acceleration fields along the trajectories of fluid particles transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. We present results for Lagrangian velocity structure functions, the acceleration probability density function, and the acceleration variance conditioned on the instantaneous velocity. These are compared with predictions of the multifractal formalism, and its merits and limitations are discussed.

High resolution DNS of shear-convective turbulence and its implications to second-order parameterizations

Shear-convective turbulence is studied using a high resolution 3D direct numerical simulation (DNS). Flow configuration consisting of a modeled jet capping a thermally unstable layer is simulated and the results are compared with the reference situation where only the convective layer is present. Quasi-equilibrium turbulent datasets, in which the turbulent energy budgets are nearly balanced, are obtained. A ‘mechanical’ barrier is identified near the jet centerline in the shear-convective case. Intense and elongated vorticity regions are created in a narrow layer above the barrier in a way similar to the shear-sheltering effect. Vertical profiles of turbulence statistics and budgets are presented. We have unambiguously identified layers of counter-gradient momentum and heat fluxes which occur near regions of penetrative convection. Using quasi-equilibrium DNS datasets, we evaluate the performance of some popular second-order closure models of turbulence. The models satisfactorily predict the triple moments and dissipation, except in the counter-gradient region. The models, however, fail to predict the pressure correlation terms.

Statistics of a passive scalar in homogeneous turbulence

Statistics of a passive scalar with Sc=1 transported by steady homogeneous turbulence at Rλ=427 and Pλ=427 is studied by using high-resolution direct numerical simulation. The Obukhov–Corrsin constant of the three-dimensional scalar spectrum in the inertial-convective range is found to be 0.68±0.04. It is proved that the -law for the scalar-velocity triple correlation holds in both inertial-convective and viscous-convective ranges when Sc>1, and found that the -law is approached with increase in Péclet number. Structure functions of the passive scalar increment and their local scaling exponents are computed as functions of the separation distance, and it is found that there exist two scaling ranges: the inertial-convective range and a narrow precursory range to the viscous-convective range. The scaling exponents in the inertial-convective range are found to be smaller than those of the velocity field and do not saturate, whereas they saturate at about 1.5 in the short precursory range to the viscous-convective range. It is also found that, contrary to the scalar case, the mixed scalar velocity structure function has a well-developed single scaling range. The scalar and scalar dissipation fields are visualized and compared with the kinetic energy dissipation field. The scalar field has a particular shape with a large-scale plateau, sharp cliff and deep valley, a mesa-canyon structure.

Large-eddy simulation of conductive flows at low magnetic Reynolds number

Using the method of large-eddy simulation, we study decaying homogeneous turbulence of a conductive flow under the influence of an applied external magnetic field at low magnetic Reynolds number. In order to assess the performance of large-eddy simulation, comparison with high resolution (5123) direct numerical simulation is performed. Results show that the modeling of subgrid scales using the dynamic Smagorinsky model is very effective in the present context.

Large scale inhomogeneity of inertial particles in turbulent flows

Preferential concentration of inertial particles in turbulent flow is studied by high resolution direct numerical simulations of two-dimensional turbulence. The formation of network-like regions of high particle density, characterized by a length scale which depends on the Stokes number of inertial particles, is observed. At smaller scales, the size of empty regions appears to be distributed according to a universal scaling law.

DNS and experiments of flow past a wired cylinder at low Reynolds number

We have performed high resolution direct numerical simulations (DNS) at Reynolds number Re=50, 160 and 500 for flow past a wired cylinder. Comparisons with companion PIV measurements made at Re=160 validate the DNS results. It is found that at Re=160 and Re=500 vortex shedding is suppressed substantially while the drag force decreases compared to a smooth cylinder flow.

Low-dimensional dynamical systems for a wake-type shear flow with vortex dislocations

Low-dimensional systems are constructed to investigate dynamics of vortex dislocations in a wake-type shear flow. High-resolution direct numerical simulations are employed to obtain flow snapshots from which the most energetic modes are extracted using proper orthogonal decomposition (POD). The first 10 modes are classified into two groups. One represents the general characteristics of two-dimensional wake-type shear flow, and the other is related to the three-dimensional properties or non-uniform characteristics along the span. Vortex dislocations are generated by these two kinds of coherent structures. The results from the first 20 three-dimensional POD modes show that the low-dimensional systems have captured the basic properties of the wake-type shear flow with vortex dislocation, such as two incommensurable frequencies and their beat frequency.

Response to “Comment on ‘Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation’ ” [Phys. Fluids 15, 1815 (2003)

Abstract

Comment on “Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation” [Phys. Fluids 14, 1065 (2002)

Comment on “Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation” [Phys. Fluids 14, 1065 (2002)

Intermittency in the joint cascade of energy and helicity.

The statistics of the energy and helicity fluxes in isotropic turbulence are studied using high resolution direct numerical simulation. The scaling exponents of the energy flux agree with those of the transverse velocity structure functions through refined similarity hypothesis, consistent with Kraichnan's prediction. The helicity flux is even more intermittent than the energy flux. Consistent with this observation, the spatial helicity-flux structures are finer than those of energy flux and more tubelike in geometry.

High resolution DNS of jet stream generated tropopausal turbulence

Tropopausal turbulence (TT), generated by jet streams, is examined, for different nonhomogeneous basic state forcing profiles, through high resolution three‐dimensional (3D) direct numerical simulations (DNS). Turbulent core regions, on either side of the jet, are characterized by a dramatic decrease in Brunt‐Väisälä frequency (N), minima in gradient Richardson number (Rig) and shear length scales, and maxima in buoyancy Reynolds number and buoyancy length scales. The edges of turbulent mixing layers are marked by N2‐bulges, which provides an alternate mechanism for multiple tropopauses. While temperature variance peaks in the vicinity of these N2‐bulges, velocity variances peak within the turbulent core. Multiple branches in the scaling of flux Richardson number with Rig are found typical for TT, a result having implications to the problem of turbulence parameterization.