Modulational instability and recurrence of hydrodynamic waves with frequency-dependent dissipation #

Alberto Alberello, Emilian Parau

14:10 Monday in 2Q42.

Part of the Advances in water waves and free-surface flows session.

Abstract #

The nonlinear Schroedinger equation (NLS) is a model for ocean waves that accurately describes the growth-decay cycles of unstable modes. In this talk we use a dissipative NLS (dNLS) with frequency-dependent dissipation to model the evolution of one carrier wave subjected to sidebands perturbation. The setup reproduces a Southern Ocean swell propagating into the marginal ice zone. Recurrence of the growth-decay cycles of the modulational instability is preserved also in the presence of dissipation, but in its phase-shifted form. Symmetry between the first order left and right sideband is broken due to the differential attenuation rate.