Stratified turbulence forced with columnar dipoles: numerical study

Augier, Pierre; Billant, Paul; Chomaz, Jean‐Marc

doi:10.1017/jfm.2015.76

Cited by 30 publications

(60 citation statements)

References 56 publications

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“…This physically means that there is an exchange of potential energy back to kinetic energy at the small scales of the turbulence. We observed this phenomenon in all simulations with F r < 1 and it has already been reported in other studies of strongly stratified turbulence such as in Augier et al (2015). The good collapse of compensated E B (k) spectra gives support to the theoretical predictions of the scaling analysis.…”

Section: Buoyancy Flux and Mixing At High F Rsupporting

confidence: 89%

Mixing efficiency in stratified turbulence

2016

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We consider mixing of the density field in stratified turbulence and argue that, at sufficiently high Reynolds numbers, stationary turbulence will have a mixing efficiency and closely related mixing coefficient described solely by the turbulent Froude number$Fr={\it\epsilon}_{k}/(Nu^{2})$, where${\it\epsilon}_{k}$is the kinetic energy dissipation,$u$is a turbulent horizontal velocity scale and$N$is the Brunt–Väisälä frequency. For$Fr\gg 1$, in the limit of weakly stratified turbulence, we show through a simple scaling analysis that the mixing coefficient scales as${\it\Gamma}\propto Fr^{-2}$, where${\it\Gamma}={\it\epsilon}_{p}/{\it\epsilon}_{k}$and${\it\epsilon}_{p}$is the potential energy dissipation. In the opposite limit of strongly stratified turbulence with$Fr\ll 1$, we argue that${\it\Gamma}$should reach a constant value of order unity. We carry out direct numerical simulations of forced stratified turbulence across a range of$Fr$and confirm that at high$Fr$,${\it\Gamma}\propto Fr^{-2}$, while at low$Fr$it approaches a constant value close to${\it\Gamma}=0.33$. The parametrization of${\it\Gamma}$based on$Re_{b}$due to Shihet al.(J. Fluid Mech., vol. 525, 2005, pp. 193–214) can be reinterpreted in this light because the observed variation of${\it\Gamma}$in their study as well as in datasets from recent oceanic and atmospheric measurements occurs at a Froude number of order unity, close to the transition value$Fr=0.3$found in our simulations.

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Section: Buoyancy Flux and Mixing At High F Rsupporting

confidence: 89%

Mixing efficiency in stratified turbulence

2016

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“…At this instant, there is no plateau observable on the horizontal spectrum of horizontal kinetic energy, but rather a dip at k h ≈ 20 and a bump at k h ≈ 80, similarly to what was observed by Augier et al (2015).…”

Section: Horizontal Spectra Of Horizontal Kinetic Energysupporting

confidence: 78%

“…On the other hand, forced stratified turbulence has received considerable attention, particularly in the case of numerical studies where the achievement of statistical stationarity is desirable (see e.g. Smith & Waleffe 2002;Laval, McWilliams & Dubrulle 2003;Waite & Bartello 2004;Lindborg 2006;Brethouwer et al 2007;Waite 2011;Almalkie & de Bruyn Kops 2012;Augier, Billant & Chomaz 2015). Most of the recent numerical studies of forced stratified turbulence have employed purely horizontal forcing to avoid direct excitation of IGWs, and force modes with k z = 0 to avoid selecting a vertical scale, two conditions that are hardly met in nature (neither KH instability nor IGW breaking leads to this kind of forcing).…”

Section: Introductionmentioning

confidence: 99%

Dynamics of stratified turbulence decaying from a high buoyancy Reynolds number

Maffioli

Davidson

2015

J. Fluid Mech.

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We present direct numerical simulations (DNS) of unforced stratified turbulence with the objective of testing the strongly stratified turbulence theory. According to this theory the characteristic vertical scale of the turbulence is given by v ∼ u h /N, where u h is the horizontal velocity scale and N the Brunt-Väisälä frequency. Combined with the hypothesis of the energy dissipation rate scaling as ∼ u 3 h / h , this theory predicts inertial range scalings for the horizontal spectrum of horizontal kinetic energy and of potential energy, according to E(k h ) ∝ k −5/3 h . We begin by presenting a scaling analysis of the horizontal vorticity equation from which we recover the result regarding the vertical scale, v ∼ u h /N, highlighting in the process the important dynamical role of large-scale vertical shear of horizontal velocity. We then present the results from decaying DNS, which show a good agreement with aspects of the theory. In particular, the vertical Froude number is found to reach a constant plateau in time, of the formin all the runs. The derivation of the dissipation scaling ∼ u 3 h / h at low Reynolds number in the context of decaying stratified turbulence highlights that the same scaling holds at high R = ReFr 2 h 1 as well as at low R 1, which is known (see Brethouwer et al., J. Fluid Mech., vol. 585, 2007, pp. 343-368) but not sufficiently emphasized in recent literature. We find evidence in our DNS of the dissipation scaling holding at R = O(1), which we interpret as being in the viscous regime. We also find k ∼ u 3 h / h and p ∼ u 3 h / h (with = k + p ), in our high-resolution run at earlier times corresponding to R = O(10), which is in the transition between the strongly stratified and the viscous regimes. The horizontal spectrum of horizontal kinetic energy collapses in time using the scaling E h (k h ) = C 1 2/3 k k −5/3 h and the horizontal potential energy spectrum is well described byThe presence of an inertial range in the horizontal direction is confirmed by the constancy of the energy flux spectrum over narrow ranges of k h . However, the vertical energy spectrum is found to differ significantly from the expected E h (k v ) ∼ N 2 k −3 v scaling, showing that Fr v is not of order unity on a scale-by-scale basis, thus providing motivation for further investigation of the vertical structure of stratified turbulence.

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“…Several other forcing mechanisms have been put forward in the literature, such as 2D forcing [69,70], as well as an assembly of vortex dipoles [71]. Each deserves separate studies in view of the complexity of these flows, and of the several characteristic scales in the system, as well as the different inertial ranges that have to be resolved a priori.…”

Section: Discussionmentioning

confidence: 99%

Large-scale anisotropy in stably stratified rotating flows

et al. 2014

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We present results from direct numerical simulations of the Boussinesq equations in the presence of rotation and/or stratification, both in the vertical direction. The runs are forced isotropically and randomly at small scales and have spatial resolutions of up to 1024 3 grid points and Reynolds numbers of ≈ 1000. We first show that solutions with negative energy flux and inverse cascades develop in rotating turbulence, whether or not stratification is present. However, the purely stratified case is characterized instead by an early-time, highly anisotropic transfer to large scales with almost zero net isotropic energy flux. This is consistent with previous studies that observed the development of vertically sheared horizontal winds, although only at substantially later times. However, and unlike previous works, when sufficient scale separation is allowed between the forcing scale and the domain size, the total energy displays a perpendicular (horizontal) spectrum with power law behavior compatible with ∼ k −5/3 ⊥ , including in the absence of rotation. In this latter purely stratified case, such a spectrum is the result of a direct cascade of the energy contained in the large-scale horizontal wind, as is evidenced by a strong positive flux of energy in the parallel direction at all scales including the largest resolved scales.

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Stratified turbulence forced with columnar dipoles: numerical study

Cited by 30 publications

References 56 publications

Mixing efficiency in stratified turbulence

Mixing efficiency in stratified turbulence

Dynamics of stratified turbulence decaying from a high buoyancy Reynolds number

Large-scale anisotropy in stably stratified rotating flows

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