Generation of slow large scales in forced rotating stratified turbulence

Smith, Leslie; Waleffe, Fabian

doi:10.1017/s0022112001006309

Cited by 199 publications

(296 citation statements)

References 37 publications

(69 reference statements)

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“…2, two spectra are presented, for the simulations with isotropic forcing and Fr ≈ 0.02 and ≈ 0.01. As stratification is increased, energy distribution becomes more anisotropic, with energy being preferentially trans- ferred towards modes with smaller k ⊥ (and, as a result, larger wave period) [20][21][22]27]. However, for Fr ≈ 0.01 energy accumulates near the modes with wave period (τ ω ∝ 1/ω 0 ) equal to the nonlinear turnover time (τ NL ∝ L/u rms ), forming a ridge.…”

Section: A Spatial Spectral Analysismentioning

confidence: 99%

“…However, for Fr ≈ 0.01 energy accumulates near the modes with wave period (τ ω ∝ 1/ω 0 ) equal to the nonlinear turnover time (τ NL ∝ L/u rms ), forming a ridge. As the energy transfer mechanism is often given by the shortest timescale [43], modes below the curve τ ω = τ NL (those with wave period shorter than the turnover time) are associated with waves [21,22,27]. Modes above the curve τ ω = τ NL (and in particular, modes with k ⊥ = 0) are often called vortical modes, as for these modes ω 0 ≈ 0.…”

Section: A Spatial Spectral Analysismentioning

confidence: 99%

“…But results for purely stratified turbulence are unclear. It is known that stratified flows can generate large-scale vertically sheared horizontal winds (VSHW) [27], although the mechanism involved is not entirely understood. While evidence of energy flow toward large scales has been reported [28,29], several authors have argued that an inverse cascade is not possible [21,30] based on statistical mechanical arguments.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: A Spatial Spectral Analysismentioning

confidence: 99%

Section: A Spatial Spectral Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Absorption of waves by large-scale winds in stratified turbulence

Leoni

Mininni

2015

Phys. Rev. E

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“…(In previous works studying turbulence in rotating stratified flows (e.g. Smith & Waleffe 2002), an isotropic grid in x, y, and z was used, regardless of the value of N/f .) A more conventional purely pseudo-spectral version of the algorithm evolving the full vector A has also been developed to demonstrate the advantages of explicit PV conservation in the present 'hybrid' CASL algorithm.…”

Section: Appendix the Numerical Algorithmmentioning

confidence: 99%

A balanced approach to modelling rotating stably stratified geophysical flows

Dritschel

Viúdez²

2003

J. Fluid Mech.

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We describe a new approach to modelling three-dimensional rotating stratified flows under the Boussinesq approximation. This approach is based on the explicit conservation of potential vorticity, and exploits the underlying leading-order geostrophic and hydrostratic balances inherent in these equations in the limit of small Froude and Rossby numbers. These balances are not imposed, but instead are used to motivate the use of a pair of new variables expressing the departure from geostrophic and hydrostratic balance. These new variables are the ageostrophic horizontal vorticity components, i.e. the vorticity not directly associated with the displacement of isopycnal surfaces. The use of potential vorticity and ageostrophic horizontal vorticity, rather than the usual primitive variables of velocity and density, reveals a deep mathematical structure and appears to have advantages numerically. This change of variables results in a diagnostic equation, of Monge-Ampère type, for one component of a vector potential ϕ, and two Poisson equations for the other two components. The curl of ϕ gives the velocity field while the divergence of ϕ is proportional to the displacement of isopycnal surfaces. This diagnostic equation makes transparent the conditions for both static and inertial stability, and may change form from (spatially) elliptic to (spatially) hyperbolic even when the flow is statically and inertially stable. A numerical method based on these new variables is developed and used to examine the instability of a horizontal elliptical shear zone (modelling a jet streak). The basic-state flow is in exact geostrophic and hydrostratic balance. Given a small perturbation however, the shear zone destabilizes by rolling up into a street of vortices and radiating inertia-gravity waves.

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“…Extensive numerical studies of rotating turbulence, stratified turbulence and turbulence with both rotations and stratification were performed 12,13,14,15 . Accumulation of energy at the horizontally largest scales were reported in direct numerical simulations 13,14 . The accumulation in the rotating strong turbulence happens presumably owing to the inverse cascade of two-dimensional turbulence.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear wave–wave interactions in stratified flows: Direct numerical simulations

Lvov

Yokoyama

2009

Physica D: Nonlinear Phenomena

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To investigate the formation mechanism of energy spectra of internal waves in the oceans, direct numerical simulations are performed. The simulations are based on the reduced dynamical equations of rotating stratified turbulence. In the reduced dynamical equations only wave modes are retained, and vortices and horizontally uniform vertical shears are excluded. Despite the simplifications, our simulations reproduce some key features of oceanic internal-wave spectra: accumulation of energy at near-inertial waves and realistic frequency and horizontal wavenumber dependencies. Furthermore, we provide evidence that formation of the energy spectra in the inertial subrange is dominated by scale-separated interactions with the near-inertial waves. These findings support observationallybased intuition that spectral energy density of internal waves is the result of predominantly wavewave interactions.

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Generation of slow large scales in forced rotating stratified turbulence

Cited by 199 publications

References 37 publications

Absorption of waves by large-scale winds in stratified turbulence

Absorption of waves by large-scale winds in stratified turbulence

A balanced approach to modelling rotating stably stratified geophysical flows

Nonlinear wave–wave interactions in stratified flows: Direct numerical simulations

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