THREE DIMENSIONAL FULLY LOCALIZED WAVES ON ICE-COVERED OCEAN

We have recently shown [1] that fully-localized three-dimensional wave envelopes (so-called dromions) can exist and propagate on the surface of ice-covered waters. Here we show that the inertia of the ice can play an important role in the size, direction and speed of propagation of these structures. We use multiple-scale perturbation technique to derive governing equations for the weakly nonlinear envelope of monochromatic waves propagating over the ice-covered seas. We show that the governing equations simplify to a coupled set of one equation for the envelope amplitude and one equation for the underlying mean current. This set of nonlinear equations can be further simplified to fall in the category of Davey-Stewartson equations [2]. We then use a numerical scheme initialized with the analytical dromion solution of DSI (i.e. shallow-water and surface-tension dominated regimes of Davey-Stewartson equation) to look for dromion solution of our equations. Dromions can travel over long distances and can transport mass, momentum and energy from the ice-edge deep into the solid ice-cover that can result in the ice cracking/breaking and also in posing dangers to icebreaker ships.