A two-dimensional Boussinesq model of the thermohaline convection
in a rectangular
domain is forced at the top by a prescribed temperature and a prescribed
salinity
flux. The two forcings have opposite effects on the density field, which
leads to the
formation of fronts and multiple equilibria. Numerical results
are interpreted through
a comparison with the solutions of an asymptotic equation, derived in the
limit of a
shallow basin by Cessi & Young (1992). In order to
explain the discrepancies between
the numerical and the asymptotic solutions, we extend this asymptotic approach
through a geometrical representation and a topological classification of
the surface
forcings. By comparing three forcings, we propose a global picture which
gives clues
to interpret the numerical solutions.