Titre/Title : Three-dimensional Dynamics of Internal Gravity Wave Beams in Stratified Flows
Contact : Chantal Staquet (équipe MEIGE)
Résumé/Abstract : Internal gravity wave beams (IGWB) are time-harmonic plane waves with general spatial profile. Such disturbances arise in fluids with continuous stratification in the vertical as a result of the inherent anisotropy of internal wave motion in this setting, and may be regarded as the analogues of cylindrical wave fronts in isotropic media. IGWB are of considerable geophysical interest, as they form the backbone of the ocean internal tide induced by the interaction of the barotropic tide with sea-floor topography, and can be also generated in the atmosphere due to thunderstorms.
Prior theoretical studies of IGWB have considered mostly two-dimensional disturbances in an inviscid Boussinesq fluid with constant buoyancy frequency. Under these flow conditions, isolated uniform IGWB happen to be exact nonlinear states irrespective of the beam profile, and significant nonlinear interactions are limited to reflections at boundaries and possibly collisions of beams. This talk will describe recent joint work with Takeshi Kataoka (Kobe University, Japan) on the three-dimensional dynamics of IGWB.
The three-dimensional propagation of IGWB differs fundamentally from its two-dimensional counterpart. Three-dimensional variations enable resonant transfer of energy, through the action of Reynolds stresses, to the flow mean potential vorticity, thus resulting in strong nonlinear coupling between an IGWB and its induced mean flow. It turns out that this coupling mechanism is described by a system of two nonlinear equations, which governs asymptotically the beam—mean-flow evolution in three dimensions. This relatively simple model explains the salient features of the experimental observations by Bordes et al. (2012) of a strong horizontal mean flow accompanying an IGWB of limited lateral extent. In addition, the interaction of IGWB with the induced mean flow can trigger instability of uniform IGWB to three-dimensional perturbations. This type of modulational instability is central to three-dimensional IGWB dynamics, in contrast to the widely-studied parametric subharmonic instability (PSI) of sinusoidal wavetrains, which is relevant to beams with nearly monochromatic profile only.