Detailed investigation of energy transfers in homogeneous stratified turbulence*

Godeferd, Fabien S.; Cambon, Claude

doi:10.1063/1.868214

Cited by 126 publications

(133 citation statements)

References 17 publications

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“…It is consistent with energy accumulation in the vicinity of k 3 for every energy component and with the results obtained from EDQNM by Godeferd & Cambon [25] ( fig. 1 in their paper) and by Sagaut & Cambon [32] (fig.…”

Section: (B) Energy Anisotropizationsupporting

confidence: 80%

“…This tendency corresponds to the formation of a two-component flow as the third, vertical, component collapses. Godeferd & Cambon [25] and Sagaut & Cambon [32] provided a thorough investigation of this behaviour.…”

Section: (B) Energy Anisotropizationmentioning

confidence: 99%

“…The QNSE, as well as other spectral theories [25], is formulated for a three-dimensional turbulent flow with imposed vertical stabilizing temperature gradient. The flow is governed by the momentum, temperature and continuity equations in the Boussinesq approximation,…”

Section: Model Outlinementioning

confidence: 99%

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An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

Sukoriansky

Galperin

2013

Phil. Trans. R. Soc. A.

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The buoyancy subrange of stably stratified turbulence is defined as an intermediate range of scales larger than those in the inertial subrange. This subrange encompasses the crossover from internal gravity waves (IGWs) to small-scale turbulence. The energy exchange between the waves and small-scale turbulence is communicated across this subrange. At the same time, it features progressive anisotropization of flow characteristics on increasing spatial scales. Despite many observational and computational studies of the buoyancy subrange, its theoretical understanding has been lagging. This article presents an investigation of the buoyancy subrange using the quasi-normal scale elimination (QNSE) theory of turbulence. This spectral theory uses a recursive procedure of small-scale modes elimination based upon a quasi-normal mapping of the velocity and temperature fields using the Langevin equations. In the limit of weak stable stratification, the theory becomes completely analytical and yields simple expressions for horizontal and vertical eddy viscosities and eddy diffusivities. In addition, the theory provides expressions for various one-dimensional spectra that quantify turbulence anisotropization. The theory reveals how the dispersion relation for IGWs is modified by turbulence, thus alleviating many unique waves' features. Predictions of the QNSE theory for the buoyancy subrange are shown to agree well with various data.

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Section: (B) Energy Anisotropizationsupporting

confidence: 80%

Section: (B) Energy Anisotropizationmentioning

confidence: 99%

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An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

Sukoriansky

Galperin

2013

Phil. Trans. R. Soc. A.

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“…c 1 corresponds to a 'vertical vortex' or toroidal mode, whereas c 2 corresponds to a wave or poloidal mode. Incompressible solutions of equations (12) and (13) in Fourier space and in the Craya-Herring frame are (Godeferd & Cambon, 1994):…”

Section: Linearised Boussinesq Equations With Rotationmentioning

confidence: 99%

Kinematic simulation for stably stratified and rotating turbulence

Nicolleau

Vassilicos

2008

Fluid Dyn. Res.

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The properties of one-particle and particle-pair diffusion in rotating and stratified turbulence are studied by applying the Rapid Distortion Theory to a Kinematic Simulation of the Boussinesq equation with a Coriolis term.Scalings for one-and two-particle horizontal and vertical diffusions in purely rotating turbulence are proposed for small Rossby numbers.Particular attention is given to the locality-in-scale hypothesis for two-particle diffusion in purely rotating turbulence both in the horizontal and the vertical directions. It is observed that both rotation and stratification decrease the pair diffusivity and improve the validity of the locality-in-scale hypothesis. In the case of stratification the range of scales over which the locality-in-scale hypothesis is observed is increased.It is found that rotation decreases the diffusion in the horizontal direction as well as, though to a much lesser extent, in the vertical direction.

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“…On the other hand, the numerical treatment of the angular dependence of E (k, t) and Z(k, t) remains a challenge. As an example, the numerical cost of axisymmetric EDQNM models (Godeferd & Cambon 1994;Bellet et al 2006;Favier et al 2011) is much higher than that of the basic EDQNM for isotropic turbulence. These models were developed, from the first case of rotating turbulence (Cambon & Jacquin 1989), for flows dominated by interacting dispersive waves and without explicit linear effect in the governing equation for the energy density E (k, t), requiring the use of the most complicated EDQNM version to handle the effects induced by the mean flow on triple correlations, such as the inhibition of the energy cascade in the case of rotating flows.…”

mentioning

confidence: 99%

A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors

2015

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International audienceA nonlinear spectral model in terms of spherically averaged descriptors is derived for the prediction of homogeneous turbulence dynamics in the presence of arbitrary mean-velocity gradients. The governing equations for the tensor $\hat{R}_{ij}(\mathbf k,t)$, the Fourier transform of the two-point second-order correlation tensor, are first closed by an anisotropic eddy-damped quasinormal Markovian procedure. This closure is restricted to turbulent flows where linear effects induced by mean-flow gradients have no essential qualitative effects on the dynamics of triple correlations compared with the induced production effects in the equations for second-order correlations. Truncation at the first relevant order of spectral angular dependence allows us to derive from these equations in vector $\mathbf k$ our final model equations in terms of the wavenumber modulus $k$ only. Analytical spherical integration results in a significant decrease in computational cost. Besides, the model remains consistent with the decomposition in terms of directional anisotropy and polarization anisotropy, with a spherically averaged anisotropic spectral tensor for each contribution. Restriction of anisotropy to spherically averaged descriptors, however, entails a loss of information, and realizability conditions are considered to quantify the upper boundary of anisotropy that can be investigated with the proposed model. Several flow configurations are considered to assess the validity of the present model. Satisfactory agreement with experiments on grid-generated turbulence subjected to successive plane strains is observed, which confirms the capability of the model to account for production of anisotropy by mean-flow gradients. The nonlinear transfer terms of the model are further tested by considering the return to isotropy (RTI) of different turbulent flows. Different RTI rates for directional anisotropy and polarization anisotropy allow us to correctly predict the apparent delayed RTI shown after axisymmetric expansion. The last test case deals with homogeneous turbulence subjected to a constant pure plane shear. The interplay between linear and nonlinear effects is reproduced, yielding the eventual exponential growth of the turbulent kinetic energy

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Detailed investigation of energy transfers in homogeneous stratified turbulence*

Cited by 126 publications

References 17 publications

An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

Kinematic simulation for stably stratified and rotating turbulence

A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors

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