Double diffusive instability in a tall thin slot

The linear stability of doubly diffusive convection is considered for a two -dimensional, Boussinesq fluid in a tall thin slot. For a variety of bounda ry conditions on the slot walls, instability sets in through zero wavenumbe r over a wide range of physical conditions. Long-wave equations governing t he nonlinear development of the instability are derived. The form of the lo ng-wave equations sensitively depends on the thermal and salt boundary cond itions; the possible long-wave theories are catalogued. Finite-amplitude so lutions and their stability are studied. In some cases the finite-amplitude solutions are not the only possible attractors and numerical solutions pre senting the alternatives are given. These reveal temporally complicated dyn amics.