Geostrophic Adjustment and Inverse Cascades in Rotating Stratified Turbulence

Bartello, Peter

doi:10.1175/1520-0469(1995)052<4410:gaaici>2.0.co;2

Cited by 233 publications

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“…The slow zero eigenvalue modes in the general (rotating and stratified) case in a periodic box with no mean flow have a more complex expression, see e.g., [37,50]. This further explains why we use 3D forcing, as using 2D forcing would favor direct injection of energy only in the slow modes in the purely rotating case, and in a combination of slow and fast (wave) modes in any other case.…”

Section: Simulations Of Rotating and Stratified Flowsmentioning

confidence: 99%

“…Conclusions from simulations are sometimes contradictory and depend on whether the flow also rotates or not. When rotation and stratification are comparable, inverse cascades have been observed [37][38][39][40]. In this case, helicity is also created in the flow [41,42], and can be responsible for the socalled anisotropic kinetic alpha effect instability [43], as well as for other large-scale instabilities [44,45].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Simulations Of Rotating and Stratified Flowsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Large-scale anisotropy in stably stratified rotating flows

et al. 2014

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“…The limit ageostrophic (2.14) is derived from both resonant ( w AG , w QG , w AG ) and ( w QG , w AG , w AG ) triads as well as the strict 3-wave resonances (w AG , w AG , w AG ). Notice that the slow-fast-slow (w QG , w AG , w QG ) triads are not resonant to the lowest order in 1/N and appear only at the next order in 1/N via 4-wave resonances (see also [18]). …”

Section: The Limit Resonant Equationsmentioning

confidence: 99%

Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics

2000

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Abstract. Fast singular oscillating limits of the three-dimensional "primitive" equations of geophysical fluid flows are analyzed. We prove existence on infinite time intervals of regular solutions to the 3D "primitive" Navier-Stokes equations for strong stratification (large stratification parameter N). This uniform existence is proven for periodic or stress-free boundary conditions for all domain aspect ratios, including the case of three wave resonances which yield nonlinear "2 1 2 dimensional" limit equations for N → +∞; smoothness assumptions are the same as for local existence theorems, that is initial data in Hα, α ≥ 3/4. The global existence is proven using techniques of the Littlewood-Paley dyadic decomposition. Infinite time regularity for solutions of the 3D "primitive" Navier-Stokes equations is obtained by bootstrapping from global regularity of the limit resonant equations and convergence theorems.Mathematics Subject Classification. 76D05, 76D50, 76U05, 86A10.

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“…As already mentioned, an inverse cascade is a self-similar process by which energy is transferred nonlinearly from small scales to larger scales, so energy gets accumulated in structures with larger correlation length than that of the injection mechanism. Inverse cascades have been ex-tensively studied in two dimensional turbulence [1], and have also been observed in rotating turbulence (including rotating stratified turbulence) [24][25][26]. But results for purely stratified turbulence are unclear.…”

Section: Introductionmentioning

confidence: 99%

Absorption of waves by large-scale winds in stratified turbulence

Leoni

Mininni

2015

Phys. Rev. E

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The atmosphere is a nonlinear stratified fluid in which internal gravity waves are present. These waves interact with the flow, resulting in wave turbulence that displays important differences with the turbulence observed in isotropic and homogeneous flows. We study numerically the role of these waves and their interaction with the large scale flow, consisting of vertically sheared horizontal winds. We calculate their space and time resolved energy spectrum (a four-dimensional spectrum), and show that most of the energy is concentrated along a dispersion relation that is Doppler shifted by the horizontal winds. We also observe that when uniform winds are let to develop in each horizontal layer of the flow, waves whose phase velocity is equal to the horizontal wind speed have negligible energy. This indicates a nonlocal transfer of their energy to the mean flow. Both phenomena, the Doppler shift and the absorption of waves traveling with the wind speed, are not accounted for in current theories of stratified wave turbulence.

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Geostrophic Adjustment and Inverse Cascades in Rotating Stratified Turbulence

Cited by 233 publications

References 0 publications

Large-scale anisotropy in stably stratified rotating flows

Large-scale anisotropy in stably stratified rotating flows

Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics

Absorption of waves by large-scale winds in stratified turbulence

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