INTERNAL GRAVITY WAVES: From Instabilities to Turbulence

Abstract

We review the mechanisms of steepening and breaking for internal gravity waves in a continuous density stratification. After discussing the instability of a plane wave of arbitrary amplitude in an infinite medium at rest, we consider the steepening effects of wave reflection on a sloping boundary and propagation in a shear flow. The final process of breaking into small-scale turbulence is then presented. The influence of those processes upon the fluid medium by mean flow changes is discussed. The specific properties of wave turbulence, induced by wave-wave interactions and breaking, are illustrated by comparative studies of oceanic and atmospheric observations, as well as laboratory and numerical experiments. We then review the different attempts at a statistical description of internal gravity wave fields, whether weakly or strongly interacting.

Absorption of waves by large-scale winds in stratified turbulence

“…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].…”

Large-scale anisotropy in stably stratified rotating flows

“…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.…”

Applications of Lie Group Analysis to Mathematical Modelling in Natural Sciences

“…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.…”

“…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.…”