scholarly journals Waves and vortices in the inverse cascade regime of stratified turbulence with or without rotation

2016 ◽  
Vol 806 ◽  
pp. 165-204 ◽  
Author(s):  
Corentin Herbert ◽  
Raffaele Marino ◽  
Duane Rosenberg ◽  
Annick Pouquet
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Vertical Shear ◽  
Energy Spectra ◽  
Stratified Turbulence ◽  
Viscous Effects ◽  
Inverse Cascade ◽  
Main Effects ◽  
The Waves

We study the partition of energy between waves and vortices in stratified turbulence, with or without rotation, for a variety of parameters, focusing on the behaviour of the waves and vortices in the inverse cascade of energy towards the large scales. To this end, we use direct numerical simulations in a cubic box at a Reynolds number $Re\approx 1000$, with the ratio between the Brunt–Väisälä frequency $N$ and the inertial frequency $f$ varying from $1/4$ to 20, together with a purely stratified run. The Froude number, measuring the strength of the stratification, varies within the range $0.02\leqslant Fr\leqslant 0.32$. We find that the inverse cascade is dominated by the slow quasi-geostrophic modes. Their energy spectra and fluxes exhibit characteristics of an inverse cascade, even though their energy is not conserved. Surprisingly, the slow vortices still dominate when the ratio $N/f$ increases, also in the stratified case, although less and less so. However, when $N/f$ increases, the inverse cascade of the slow modes becomes weaker and weaker, and it vanishes in the purely stratified case. We discuss how the disappearance of the inverse cascade of energy with increasing $N/f$ can be interpreted in terms of the waves and vortices, and identify the main effects that can explain this transition based on both inviscid invariants arguments and viscous effects due to vertical shear.

scholarly journals Partitioning Waves and Eddies in Stably Stratified Turbulence

Atmosphere ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 420 ◽  
Author(s):  
Henri Lam ◽  
Alexandre Delache ◽  
Fabien S Godeferd
Keyword(s):  
Dispersion Relation ◽  
Kinetic Energy ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Energy Concentration ◽  
Kinetic Energy Density ◽  
Stratified Turbulence ◽  
The Waves

We consider the separation of motion related to internal gravity waves and eddy dynamics in stably stratified flows obtained by direct numerical simulations. The waves’ dispersion relation links their angle of propagation to the vertical θ , to their frequency ω , so that two methods are used for characterizing wave-related motion: (a) the concentration of kinetic energy density in the ( θ , ω ) map along the dispersion relation curve; and (b) a direct computation of two-point two-time velocity correlations via a four-dimensional Fourier transform, permitting to extract wave-related space-time coherence. The second method is more computationally demanding than the first. In canonical flows with linear kinematics produced by space-localized harmonic forcing, we observe the pattern of the waves in physical space and the corresponding concentration curve of energy in the ( θ , ω ) plane. We show from a simple laminar flow that the curve characterizing the presence of waves is distorted differently in the presence of a background convective mean velocity, either uniform or varying in space, and also when the forcing source is moving. By generalizing the observation from laminar flow to turbulent flow, this permits categorizing the energy concentration pattern of the waves in complex flows, thus enabling the identification of wave-related motion in a general turbulent flow with stable stratification. The advanced method (b) is finally used to compute the wave-eddy partition in the velocity–buoyancy fields of direct numerical simulations of stably stratified turbulence. In particular, we use this splitting in statistics as varied as horizontal and vertical kinetic energy, as well as two-point velocity and buoyancy spectra.

scholarly journals Scaling analysis and simulation of strongly stratified turbulent flows

2007 ◽  
Vol 585 ◽  
pp. 343-368 ◽  
Author(s):  
G. BRETHOUWER ◽  
P. BILLANT ◽  
E. LINDBORG ◽  
J.-M. CHOMAZ
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Turbulent Flows ◽  
Scaling Laws ◽  
Three Dimensional ◽  
Direct Numerical Simulations ◽  
Small Scale ◽  
Scaling Analysis ◽  
Length Scale ◽  
Stratified Turbulence

Direct numerical simulations of stably and strongly stratified turbulent flows with Reynolds number Re ≫ 1 and horizontal Froude number Fh ≪ 1 are presented. The results are interpreted on the basis of a scaling analysis of the governing equations. The analysis suggests that there are two different strongly stratified regimes according to the parameter $\mathcal{R} \,{=}\, \hbox{\it Re} F^2_h$. When $\mathcal{R} \,{\gg}\, 1$, viscous forces are unimportant and lv scales as lv ∼ U/N (U is a characteristic horizontal velocity and N is the Brunt–Väisälä frequency) so that the dynamics of the flow is inherently three-dimensional but strongly anisotropic. When $\mathcal{R} \,{\ll}\, 1$, vertical viscous shearing is important so that $l_v \,{\sim}\, l_h/\hbox{\it Re}^{1/2}$ (lh is a characteristic horizontal length scale). The parameter $\cal R$ is further shown to be related to the buoyancy Reynolds number and proportional to (lO/η)4/3, where lO is the Ozmidov length scale and η the Kolmogorov length scale. This implies that there are simultaneously two distinct ranges in strongly stratified turbulence when $\mathcal{R} \,{\gg}\, 1$: the scales larger than lO are strongly influenced by the stratification while those between lO and η are weakly affected by stratification. The direct numerical simulations with forced large-scale horizontal two-dimensional motions and uniform stratification cover a wide Re and Fh range and support the main parameter controlling strongly stratified turbulence being $\cal R$. The numerical results are in good agreement with the scaling laws for the vertical length scale. Thin horizontal layers are observed independently of the value of $\cal R$ but they tend to be smooth for $\cal R$< 1, while for $\cal R$ > 1 small-scale three-dimensional turbulent disturbances are increasingly superimposed. The dissipation of kinetic energy is mostly due to vertical shearing for $\cal R$ < 1 but tends to isotropy as $\cal R$ increases above unity. When $\mathcal{R}$ < 1, the horizontal and vertical energy spectra are very steep while, when $\cal R$ > 1, the horizontal spectra of kinetic and potential energy exhibit an approximate k−5/3h-power-law range and a clear forward energy cascade is observed.

Potential enstrophy in stratified turbulence

2013 ◽  
Vol 722 ◽  
Author(s):  
Michael L. Waite
Keyword(s):  
Fluid Dynamics ◽  
Numerical Simulations ◽  
Reynolds Numbers ◽  
Direct Numerical Simulations ◽  
Quadratic Approximation ◽  
Stratified Turbulence ◽  
Geophysical Fluid Dynamics ◽  
Quadratic Part ◽  
Flow Variables ◽  
Potential Enstrophy

AbstractDirect numerical simulations are used to investigate potential enstrophy in stratified turbulence with small Froude numbers, large Reynolds numbers, and buoyancy Reynolds numbers ($R{e}_{b} $) both smaller and larger than unity. We investigate the conditions under which the potential enstrophy, which is a quartic quantity in the flow variables, can be approximated by its quadratic terms, as is often done in geophysical fluid dynamics. We show that at large scales, the quadratic fraction of the potential enstrophy is determined by $R{e}_{b} $. The quadratic part dominates for small $R{e}_{b} $, i.e. in the viscously coupled regime of stratified turbulence, but not when $R{e}_{b} \gtrsim 1$. The breakdown of the quadratic approximation is consistent with the development of Kelvin–Helmholtz instabilities, which are frequently observed to grow on the layerwise structure of stratified turbulence when $R{e}_{b} $ is not too small.

scholarly journals Turbulent Coagulation of Aerosol Particles: New Insights From Direct Numerical Simulations and Holographic Imaging Experiments

2003 ◽  
Author(s):  
Lance R. Collins ◽  
Hui Meng ◽  
Aruj Ahluwalia ◽  
Lujie Cao ◽  
Gang Pan
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Search Algorithm ◽  
Concentration Field ◽  
Direct Numerical Simulations ◽  
Three Dimensions ◽  
Collision Kernel ◽  
Coagulation Rate ◽  
Subsequent Work ◽  
Turbulent Fluctuations

Particle collisions driven by turbulent fluctuations play a key role in such diverse problems as cloud formation, aerosol powder manufacturing and inhalation drug therapy to name a few. In all of these examples (and many others) turbulent fluctuations increase the rate of collisions relative to the background collision rate driven by Brownian motion. Furthermore, turbulence can spontaneously generate very large fluctuations in the particle concentration field. This “clustering” is caused by the inertial mismatch between the heavy particles and the lighter surrounding gas; vortices in the flow “centrifuge” the heavier particles out of vortex cores and into the straining regions that lie in between the vortices. Because collision is a binary process, concentration fluctuations further enhance the turbulent coagulation rate by as much as two orders of magnitude. An effect of this size must be accounted for in a rational model of turbulent coagulation. Sundaram & Collins (J. Fluid Mech. 1997) showed that the radial distribution function (RDF) of the particle population, evaluated at contact, precisely corrects the collision kernel for clustering. Subsequent work has explored the dependence of the RDF on the system parameters (e.g., particle size, concentration, response time and Reynolds number) using direct numerical simulations. These results have improved our understanding and ability to predict the effect of the first three parameters; however, owing to the limited range of Reynolds number that can be reached in a numerical simulation, questions remain over the scaling of the RDF with Reynolds number. This is a critical issue for high-Reynolds-number applications such as cloud physics, where values of the Reynolds number can be 1–2 orders of magnitude greater than can be simulated. We will present our highest Reynolds number simulations to date and show our attempts to resolve this issue. Recently, the ability to measure three-dimensional particle positions using holography has been realized (e.g., Meng & Pu, J. Opt. Soc. Am. 2003). With holography, the optical image that is produced contains fringes that, upon inverting the laser, reproduce the original image in three dimensions. The hologram can then be scanned using a digital camera to obtain the particle positions. An important consideration with this study is the need to differentiate individual particles. We developed a search algorithm that locates particle centers, even in the presence of optical aberations and speckle noise. The algorithm has been used to obtain the first experimental RDF measurements to date. Thus far we see good agreement between the experimentally obtained RDF and the simulations. Besides validating the simulations, experiments can span a much broader range of Reynolds numbers, providing critical data that may help resolve the open questions associated with this parameter.

scholarly journals Comparison between experiments and direct numerical simulations in a channel flow with roughness on one wall

2008 ◽  
Vol 600 ◽  
pp. 403-426 ◽  
Author(s):  
P. BURATTINI ◽  
S. LEONARDI ◽  
P. ORLANDI ◽  
R. A. ANTONIA
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Friction Velocity ◽  
Streamwise Velocity ◽  
Negative Energy ◽  
Direct Numerical Simulations ◽  
Rough Wall ◽  
Local Isotropy ◽  
Taylor’S Hypothesis ◽  
Yielding Support

The turbulent flow in a two-dimensional channel with roughness on one wall is investigated using experiments and direct numerical simulations (DNS). The elements have a square cross-section with height k=0.1H (H is the channel half-width) and a streamwise spacing of 4k. The Reynolds number Reτr, based on the friction velocity at the rough wall and H, is in the range 300–1100. Particular attention is given to the rough-wall side. Measured turbulence intensities, length scales, leading terms in the turbulent kinetic energy budget, and velocity spectra are compared with those obtained from the DNS. Close agreement is found, yielding support for the simplifying assumptions in the experiment (notably local isotropy and Taylor's hypothesis) and the adequacy of the spatial resolution in the simulation. Overall, the profiles of the Reynolds normal stresses on the roughness side are almost independent of Reτr, when normalized by outer variables. Energy spectra at different locations above the rough wall collapse well at high wavenumbers, when normalized by Kolmogorov scales. In contrast to previous studies, a region of negative energy production near the location of the maximum streamwise velocity is not observed. Comparison with a smooth-wall channel, at similar values of the friction-velocity Reynolds number, highlights differences only in the streamwise velocity component near the wall.

Lagrangian characteristics of turbulence and scalar transport in direct numerical simulations

2001 ◽  
Vol 427 ◽  
pp. 241-274 ◽  
Author(s):  
P. K. YEUNG
Keyword(s):  
Reynolds Number ◽  
Correlation Function ◽  
Numerical Simulations ◽  
Time Scales ◽  
Time Scale ◽  
Cross Correlation ◽  
Scalar Fields ◽  
Direct Numerical Simulations ◽  
Cross Correlation Function ◽  
Differential Diffusion

A study of the Lagrangian statistical properties of velocity and passive scalar fields using direct numerical simulations is presented, for the case of stationary isotropic turbulence with uniform mean scalar gradients. Data at higher grid resolutions (up to 5123 and Taylor-scale Reynolds number 234) allow an update of previous velocity results at lower Reynolds number, including intermittency and dimensionality effects on vorticity time scales. The emphasis is on Lagrangian scalar time series which are new to the literature and important for stochastic mixing models. The variance of the ‘total’ Lagrangian scalar value (ϕ˜+, combining contributions from both mean and fluctuations) grows with time, with the velocity–scalar cross-correlation function and fluid particle displacements playing major roles. The Lagrangian increment of ϕ˜+ conditioned upon velocity and scalar fluctuations is well represented by a linear regression model whose parameters depend on both Reynolds number and Schmidt number. The Lagrangian scalar fluctuation is non-Markovian and has a longer time scale than the velocity, which is due to the strong role of advective transport, and is in contrast to results in an Eulerian frame where the scalars have shorter time scales. The scalar dissipation is highly intermittent and becomes de-correlated in time more rapidly than the energy dissipation. Differential diffusion for scalars with Schmidt numbers between 1/8 and 1 is characterized by asymmetry in the two-scalar cross-correlation function, a shorter time scale for the difference between two scalars, as well as a systematic decrease in the Lagrangian coherency spectrum up to at least the Kolmogorov frequency. These observations are consistent with recent work suggesting that differential diffusion remains important in the small scales at high Reynolds number.

scholarly journals Direct Numerical Simulations to Investigate Energy Transfer between Meso- and Synoptic Scales

2018 ◽  
Vol 75 (4) ◽  
pp. 1163-1171 ◽  
Author(s):  
Masih Eghdami ◽  
Shanti Bhushan ◽  
Ana P. Barros
Keyword(s):  
Energy Source ◽  
Energy Transfer ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Energy Spectra ◽  
Energy Sources ◽  
Synoptic Scale ◽  
2D Turbulence ◽  
Enstrophy Cascade

Abstract Understanding the development of the atmospheric energy spectrum across scales is necessary to elucidate atmospheric predictability. In this manuscript, the authors investigate energy transfer between the synoptic scale and the mesoscale using direct numerical simulations (DNSs) of two-dimensional (2D) turbulence transfer under forcing applied at different scales. First, DNS results forced by a single kinetic energy source at large scales show that the energy spectra slopes of the direct enstrophy cascade are steeper than the theoretically predicted −3 slope. Second, the presence of two inertial ranges in 2D turbulence at intermediate scales is investigated by introducing a second energy source in the meso-α-scale range. The energy spectra for the DNS with two kinetic energy sources exhibit flatter slopes that are closer to −3, consistent with the observed kinetic energy spectra of horizontal winds in the atmosphere at synoptic scales. Further, the results are independent of model resolution and scale separation between the two energy sources, with a robust transition region between the lower synoptic and the upper meso-α scales in agreement with classical observations in the upper troposphere. These results suggest the existence of a mesoscale feedback on synoptic-scale predictability that emerges from the concurrence of the direct (downscale) enstrophy transfer in the synoptic scales and the inverse (upscale) kinetic energy transfer from the mesoscale to the synoptic scale in the troposphere.

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