Stochastic approach to convective motions driven by a localized buoyancy flux in the sea

A model for the dynamics of intermittent dense water plumes in a sea initially at rest, suddenly perturbed on the air-sea surface by a series of random buoyancy inputs localized on small space and time scales is presented. It is shown that plume evolution and scaling laws are ruled by random external forcing leading to a higher time power behaviour, depending on the probability of the event 1/T; this time power hides slower internal randomness if 1/T <<1, so that plume evolution depends on the air-sea interaction statistics and its frequency. The perturbative slowing down effect of a constant stratification and the dissipative mixing effect of the viscosity are also shown.