Boundary layers and normal mode parameters in a system with double-diffusive convection at large Rayleigh numbers

Double-diffusive convection in 2D horizontally infinite layer at large Rayleigh numbers limit is considered. We rewrite basic hydrodynamical equations in a singular-perturbed form and obtain boundary layers and critical parameters for normal mode solution by multiple-scaled method. Critical Rayleigh numbers do not depend on actual form of boundary conditions, and boundary layers have characteristic width of several centimeters in the case of thermohaline convection. The results can be useful in some important oceanographical systems like thermohaline staircases or other geophysical hydrodynamics models.