Instabilities of finite-width internal wave beams: from Floquet analysis to PSI

Abstract

The parametric subharmonic instability (PSI) of finite-width internal gravity wave beams is revisited using a formal linear stability analysis based on Floquet theory. The Floquet stability eigenvalue problem is studied asymptotically in the limit where PSI arises, namely for a small-amplitude beam of frequency no longer dominate. By adopting a frame riding with the wave beam, this advection effect is factored out and it is shown that small-amplitude beams that are not generally susceptible to PSI may develop an essentially inviscid instability with broadband frequency spectrum.