Direct numerical simulations of homogeneous turbulence in density-stratified fluids

Riley, James J.; Metcalfe, Ralph W.; Weissman, Michael A.

doi:10.1063/1.33198

Cited by 189 publications

(254 citation statements)

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“…This is important because pressure disturbances are responsible for a coupling of vertical and horizontal velocity components, and for the anisotropic dispersion law of the wavy part of the flow. The solenoidal part of the horizontal field is unaffected by the wave part of the flow and remains constant in the linear inviscid limit: it corresponds to the 'vortex' part of the flow in the purely stratified case (see Riley, Metcalfe & Weissman 1981). Accordingly, complete linear solutions (which we call RDT solutions) for the velocity in terms of plane waves may be written as…”

Section: Direct Numerical Simulationmentioning

confidence: 99%

“…N ±1 are the wave modes, also called ageostrophic modes hereinafter in agreement with classic geophysical literature. The wave-vortex terminology was used by Riley et al (1981) for analysing DNS of stably stratified turbulence, whereas geostrophic and ageostrophic were terms used by Bartello (1995) and Babin, Mahalov & Nicolaenko (1998).…”

Section: Analytical Calculations Using Rdtmentioning

confidence: 99%

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Turbulent diffusion in rapidly rotating flows with and without stable stratification

et al. 2004

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In this work, three different approaches are used for evaluating some Lagrangian properties of homogeneous turbulence containing anisotropy due to the application of a stable stratification and a solid-body rotation. The two external frequencies are the magnitude of the system vorticity 2Ω,chosen vertical here, and the Brunt-Väisälä frequency N,w h i c hg i ves the strength of the vertical stratification. Analytical results are derived using linear theory for the Eulerian velocity correlations (single-point, twotime) in the vertical and the horizontal directions, and Lagrangian ones are assumed to be equivalent, in agreement with an additional Corrsin assumption used by Kaneda (2000). They are compared with results from the kinematic simulation model (KS) by Nicolleau & Vassilicos (2000), which also incorporates the wave-vortex dynamics inherited from linear theory, and directly yields Lagrangian correlations as well as Eulerian ones. Finally, results from direct numerical simulations (DNS) are obtained and compared for the rotation-dominant case B =2Ω/N = 10, the stratificationdominant case B =1/10, the non-dispersive case B =1, and pure stratification B =0 and pure rotation N =0. The last situation is shown to be singular with respect to the mixed stratified/rotating ones. We address the question of the validity of Corrsin's simplified hypothesis, which states the equivalence between Eulerian and Lagrangian correlations. Vertical correlations are found to follow this postulate, but not the horizontal ones. Consequences for the vertical and horizontal one-particle dispersion are examined. In the analytical model, the squared excursion lengths are calculated by time integrating the Lagrangian (equal to the Eulerian) two-time correlations, according to Taylor's procedure. These quantities are directly computed from fluctuating trajectories by both KS and DNS. In the case of pure rotation, the analytical procedure allows us to relate Brownian t-asymptotic laws of dispersion in both the horizontal and vertical directions to the angular phase-mixing properties of the inertial waves. If stratification is present, the inertia-gravity wave dynamics, which affects the vertical motion, yields a suppressed vertical diffusivity, but not a suppressed horizontal diffusivity, since part of the horizontal velocity field escapes wavy motion.

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Section: Direct Numerical Simulationmentioning

confidence: 99%

Section: Analytical Calculations Using Rdtmentioning

confidence: 99%

Turbulent diffusion in rapidly rotating flows with and without stable stratification

et al. 2004

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“…The horizontal velocity mode corresponding to this direction is known as non-propagating [32] or vortical [33] and can be identified with a slow manifold.…”

Section: (B) Energy Anisotropizationmentioning

confidence: 99%

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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“…In these flows, large vertical motions are inhibited by the buoyancy force, leaving only two possible modes of motion: internal gravity waves and vortices with vertical axis (Riley, Metcalfe & Weissman 1981). Laboratory experiments (Lin & Pao 1979;Hopfinger 1987;Chomaz et al 1993;Fincham, Maxworthy & Spedding 1996;Spedding, Browand & Fincham 1996;Spedding 1997;Bonnier, Eiff & Bonneton 2000), numerical simulations (Riley et al 1981;Kimura & Herring 1996) and oceanic measurements (Gregg 1987) have revealed that these vortices never have a large vertical extent, but are † Present address: …”

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confidence: 99%

Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid

2000

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This paper shows that a long vertical columnar vortex pair created by a double flap apparatus in a strongly stratified fluid is subjected to an instability distinct from the Crow and short-wavelength instabilities known to occur in homogeneous fluid. This new instability, which we name zigzag instability, is antisymmetric with respect to the plane separating the vortices. It is characterized by a vertically modulated twisting and bending of the whole vortex pair with almost no change of the dipole's crosssectional structure. No saturation is observed and, ultimately, the vortex pair is sliced into thin horizontal layers of independent pancake dipoles. For the largest BruntVäisälä frequency N =1.75 rad s −1 that may be achieved in the experiments, the zigzag instability is observed only in the range of Froude numbers: 0.13 0.21, the elliptic instability develops resulting in three-dimensional motions which eventually collapse into a relaminarized vortex pair. Irregular zigzags are then also observed to grow. The threshold for the inhibition of the elliptic instability F h0 =0.2 ± 0.01 is independent of N and in good agreement with the theoretical study of Miyazaki & Fukumoto (1992). Complete stabilization for F h0 < 0.13 is probably due to viscous effects since the associated Reynolds number is low, Re 0 < 260. In geophysical flows characterized by low Froude numbers and large Reynolds numbers, we conjecture that this viscous stabilization will occur at much lower Froude number.It is tentatively argued that this new type of instability may explain the layering widely observed in stratified turbulent flows. IntroductionFluid motions in the atmosphere and oceans are often strongly affected by stable density stratification. In these flows, large vertical motions are inhibited by the buoyancy force, leaving only two possible modes of motion: internal gravity waves and vortices with vertical axis (Riley, Metcalfe & Weissman 1981). Laboratory experiments (Lin & Pao 1979;Hopfinger 1987;Chomaz et al. 1993;Fincham, Maxworthy & Spedding 1996;Spedding, Browand & Fincham 1996;Spedding 1997;Bonnier, Eiff & Bonneton 2000), numerical simulations (Riley et al. 1981;Kimura & Herring 1996) and oceanic measurements (Gregg 1987) have revealed that these vortices never have a large vertical extent, but are † Present address:

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Direct numerical simulations of homogeneous turbulence in density-stratified fluids

Cited by 189 publications

References 8 publications

Turbulent diffusion in rapidly rotating flows with and without stable stratification

Turbulent diffusion in rapidly rotating flows with and without stable stratification

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

Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid

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