Transient diffusive boundary layers at high Rayleigh numbers in simple and double diffusive fluids: Latency time scaling for the convection onset

The onset of buoyancy driven convection in a transient boundary layer at large Rayleigh numbers is discussed theoretically by using a minimal yet powerful method proposed by Howard. The method is applied to thermal and Soret-driven convection in bulk fluid layers, in Hele-Shaw geometries and in porous media with, respectively, isothermal as well as constant heat flux boundary conditions. Scaling laws for the onset latency time and the critical boundary layer height are derived for the cases under consideration. The crossover Rayleigh numbers, above which even in a Hele-Shaw geometry the bulk scaling laws apply, are also discussed.