Nonlinear stability of modulated Horton–Rogers–Lapwood problem

Abstract Nonlinear stability theory is used to investigate free convection arising in a particular class of Horton–Rogers–Lapwood (HRL) problem. Time periodic modulation is imposed on either the temperature at the bounding surfaces or the gravitational field permeating the medium. The Brinkman model and the Boussinesq approximation govern the fluid flow. The energy formulation is followed and the Galerkin method is used to determine the relevant threshold for arbitrary values of the modulational amplitude and frequency. In general it is found that an increase in the modulational amplitude encourages convection ensuing at the threshold. The existence of a subcritical region is predicted and the importance of the nonlinear theory is established.