Titre/Title : On mean flow generation by 3D internal wave beams
Contact : Chantal Staquet (équipe MEIGE)
Résumé/Abstract : This talk is about the generation of mean flow through wave-wave interaction for internal wave beams. The first part (1) discusses an analytical solution for a 3D diffracting wave beam. In the second part (2), the theoretical generation of mean flow by a quasi-2D internal wave beam is compared with laboratory experiments.
(1) It is well known that planar inviscid 2D internal waves happen to solve the fully nonlinear Boussinesq equations because group and phase velocities are orthogonal. Strikingly, even inviscid 2D wave beams solve the nonlinear equations. The orthogonality of phase and group velocities does not hold where different beams interact. In these regions, wave-wave interaction typically generates higher harmonics and mean flow (Thorpe, 1987).
I present an analytical solution for a 3D diffracting wave beam generated by a finite-width wave maker. Surprisingly, the linear solution also satisfies the nonlinear equation in the absence of viscosity.
For weak viscosity, the diffracting wave beam generates mean vorticity where the diffraction is strongest, which in turn drives a dipole mean flow. The analytical solution allows studying the induced mean flow as a function of wavemaker width.
(2) If the wavemaker is placed between two lateral walls, then it generates a non-diffracting quasi-2D wave beam. In this case, streaming in the lateral boundary layers generates mean vorticity near the walls, which also drives a dipole mean flow. This theoretical induced mean flow is in good agreement with laboratory experiments on particle transport.