I<scp>NTERNAL</scp> G<scp>RAVITY</scp> W<scp>AVES</scp>: From Instabilities to Turbulence

Staquet, Chantal; Sommeria, Joël

doi:10.1146/annurev.fluid.34.090601.130953

Cited by 320 publications

(276 citation statements)

References 127 publications

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“…As an example, internal gravity waves arising from it are responsible for transfer of momentum between different regions of the atmosphere [2], and for transport in the oceans [3,4]. Much effort has been put in characterizing internal gravity waves and their relation with geophysical flows [5][6][7].…”

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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Section: Introductionmentioning

confidence: 99%

Absorption of waves by large-scale winds in stratified turbulence

Leoni

Mininni

2015

Phys. Rev. E

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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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“…Furthermore, mutual interactions between internal waves produce mixing in the interior of the ocean providing an important link in the presumed energy cascade from large to small scales (e.g., [40], [47]). One of the practical needs to better understand mixing processes in the ocean resides in the fact that mixing plays an important role in maintaining a gradual transition between the sun-warmed surface layer of the ocean and the upwelling cold, dense water formed at high latitudes (e.g., [49], [43], [29], [8]). The subject of mixing processes due to breaking of internal waves in the ocean and atmosphere has received much attention in recent years (see e.g.…”

Section: Internal Gravity Wave Beams In the Deep Oceanmentioning

confidence: 99%

“…This corresponds to a vertically linear density variation. While this simplification is commonly used in laboratory and theoretical studies and it is quite reasonable for the thermocline region, it is not common in the deep region of the ocean with the exception when considering short wavelengths in comparison with the scale of density changes ( [43]). At low frequencies, close to f, rotational effects are important.…”

Section: Internal Gravity Wave Beams In the Deep Oceanmentioning

confidence: 99%

Applications of Lie Group Analysis to Mathematical Modelling in Natural Sciences

Ibragimov

Ibragimov²

2012

Math. Model. Nat. Phenom.

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Abstract. Today engineering and science researchers routinely confront problems in mathematical modeling involving solutions techniques for differential equations. Sometimes these solutions can be obtained analytically by numerous traditional ad hoc methods appropriate for integrating particular types of equations. More often, however, the solutions cannot be obtained by these methods, in spite of the fact that, e.g. over 400 types of integrable second-order ordinary differential equations were summarized in voluminous catalogues. On the other hand, many mathematical models formulated in terms of nonlinear differential equations can successfully be treated and solved by Lie group methods. Lie group analysis is especially valuable in investigating nonlinear differential equations, for its algorithms act here as reliably as for linear cases. The aim of this article is, from the one hand, to provide the wide audience of researchers with the comprehensive introduction to Lie's group analysis and, from the other hand, is to illustrate the advantages of application of Lie group analysis to group theoretical modeling of internal gravity waves in stratified fluids.

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INTERNAL GRAVITY WAVES: From Instabilities to Turbulence

Cited by 320 publications

References 127 publications

Absorption of waves by large-scale winds in stratified turbulence

Absorption of waves by large-scale winds in stratified turbulence

Large-scale anisotropy in stably stratified rotating flows

Applications of Lie Group Analysis to Mathematical Modelling in Natural Sciences

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