Possible self focusing mechanism of an inertial wave

We study inertial wave-wave interaction into an incompressible inviscid rotating fluid, by analyzing a Ginzburg-Landau equation with complex coefficients (asymptotically derived from the relevant Navier-Stokes equation). We compute the wave coupling terms at different orders in wave amplitude, relying on an approximated associated Beltrami property. At third order it is shown that wave self-coupling can lead to wave self-focusing. A short comparison is made with recent experiments.