Statistical convective down motion driven by random inputs of localized buoyancy in a homogeneous sea

A model for the dynamics of dense water plumes in a homogeneous 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 here. A Lagrangian representation allows the time evolution for a single, mixing plume able to carry down dense water mass to be obtained. Moreover scaling laws are found for long times, which depend on the surface air-sea interaction statistics involved and on the forcing time scale: in this way it is shown that the asymptotic time evolution of the plumes is the result of surface heterogeneous buoyancy forcing inputs.