Low Froude number limiting dynamics for stably stratified flow with small or finite Rossby numbers

Embid, Pedro; Majda, Andrew J.

doi:10.1080/03091929808208993

Cited by 132 publications

(162 citation statements)

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“…Numerical simulations of rotating flows have also indicated a general trend towards two-dimensionalization [8,17] and some studies [9] have reported a split of the energy cascade into a downscale and an upscale process. Other studies [18] have found that, as the rotation rate increases, the flows exhibit a dynamics very similar to what is found in a 2D system, with the vertical * Corresponding author: deusebio@mech.kth.se velocity behaving as a passive scalar [19]. Bourouiba and Bartello [20] reported a strong transfer of energy from 3D modes to 2D modes at intermediate rotation rates, whereas at large rotations a decoupling of the dynamics was observed.…”

Section: Introductionmentioning

confidence: 88%

“…Even though such interactions can move energy towards the 2D plane [17], triadic resonance cannot transfer energy into/out of the k z = 0 plane, which, in fact, constitutes a closed resonant set. If only interactions among resonant triads are allowed, 2D modes should thus be dynamically decoupled from 3D modes [18,19]. Sometimes, it is advocated that nearly resonant interactions [17], for which the resonance condition is satisfied only to a certain degree, and higher-order resonance interactions [23] can explain the transfer of energy into the k z = 0 plane.…”

Section: Introductionmentioning

confidence: 99%

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Dimensional transition in rotating turbulence

et al. 2014

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In this work we investigate, by means of direct numerical hyperviscous simulations, how rotation affects the bidimensionalization of a turbulent flow. We study a thin layer of fluid, forced by a two-dimensional forcing, within the framework of the "split cascade" in which the injected energy flows both to small scales (generating the direct cascade) and to large scale (to form the inverse cascade). It is shown that rotation reinforces the inverse cascade at the expense of the direct one, thus promoting bidimensionalization of the flow. This is achieved by a suppression of the enstrophy production at large scales. Nonetheless, we find that, in the range of rotation rates investigated, increasing the vertical size of the computational domain causes a reduction of the flux of the inverse cascade. Our results suggest that, even in rotating flows, the inverse cascade may eventually disappear when the vertical scale is sufficiently large with respect to the forcing scale. We also study how the split cascade and confinement influence the breaking of symmetry induced by rotation.

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Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Dimensional transition in rotating turbulence

et al. 2014

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“…In mid-latitudes, the fact that the rotational Coriolis terms are bounded away from zero leads to a strict temporal frequency scale separation between slow potential vorticity dynamics and fast gravity waves; theorems justifying the quasi-geostrophic mid-latitude dynamics have been proved even with general unbalanced initial data for both rapidly rotating shallow water equations and completely stratified flows [3,7,8,16,15,5]. However, the proofs require constant symmetric hyperbolic coefficients for the fast-wave dynamics in order to obtain higher derivative estimates on the solution.…”

Section: Introductionmentioning

confidence: 99%

Fast Wave Averaging for the Equatorial Shallow Water Equations

Dutrifoy

Majda

2007

Communications in Partial Differential Equations

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The equatorial shallow water equations in a suitable limit are shown to reduce to zonal jets as the Froude number tends to zero. This is a theorem of a singular limit with a fast variable coefficient due to the vanishing of the Coriolis force at the equator. Although it is not possible to get uniform estimates in classical Sobolev spaces (other than L 2 ) by differentiating the system, a new method exploiting the particular structure of the fast coefficient leads to uniform estimates in slightly different functional spaces.The computation of resonances shows that fast waves may interact with a strong external forcing, introduced to mimic the effects of moisture, to create zonal jets.

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“…As a result of this variety of regimes and of the limitations in computer power, in recent years progress has been made in understanding rotating stratified flows thanks to a combination of tools, including, e.g., wave turbulence approaches [6][7][8][9], reduced equations based on asymptotic expansions in a small parameter [10][11][12][13], experiments [14][15][16][17][18], observations in the atmosphere and the ocean [19,20], and direct numerical simulations [5,[21][22][23][24] (see also the reviews in [25,26]). However, some fundamental issues have not been clarified yet.…”

Section: Introductionmentioning

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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Low Froude number limiting dynamics for stably stratified flow with small or finite Rossby numbers

Cited by 132 publications

References 20 publications

Dimensional transition in rotating turbulence

Dimensional transition in rotating turbulence

Fast Wave Averaging for the Equatorial Shallow Water Equations

Large-scale anisotropy in stably stratified rotating flows

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