Stability of impulsively-driven natural convection with unsteady base state: implications of an adiabatic boundary

Abstract

Stability conditions of a quiescent, horizontally infinite fluid layer with adiabatic bottom subject to sudden cooling from above are studied. Here, at difference from Rayleigh–Bénard convection, the temperature base state is never steady. Instability limits are studied using linear analysis while stability is analyzed using the energy method. Critical stability curves in terms of Rayleigh numbers and convection onset times were obtained for several kinematic boundary conditions. Stability curves resulting from energy and linear approaches exhibit the same temporal growth rate for large values of time, suggesting a bound for the temporal asymptotic behavior of the energy method.