Dynamics of the thermohaline circulation under wind forcing (Q1599863)

The authors study the thermohaline circulation of the oceans in a vertical meridional plane. The basic equations of such a model are the Navier-Stokes equations and convection-diffusion equations for salinity and temperature. These model equations can be reformulated in terms of the stream function for the velocity field and the density fluctuation function for salinity and temperature. If there is no external wind forcing, the authors establish that the stream and density fluctuation function decay exponentially to zero in suitable Sobolev spaces as \(t\to\infty\). They also obtain an averaging principle in case of rapidly oscillating wind forcing.