Temporal evolution of thermal convection in an initially stably-stratified horizontal fluid layer

摘要

The temporal evolution of buoyancy-driven convection in an initially quiescent and stably-stratified fluid layer confined between two horizontal plates is investigated theoretically. After the temperature of the bottom plate is increased suddenly to a higher one, buoyancy-driven convection appears at a certain time. In order to trace the related time-dependent thermal behavior, the Boussinesq equations are solved numerically by using the finite element method to examine the growth rates of the basic temperature field and its fluctuations with time. Based on the numerical results, the characteristic times to mark the onset of intrinsic instability, the first detection of convective motion and the ensuing manifestation of convection are illustrated by a set of new parameters suggested here. The latter two characteristic times are discussed in comparison with the experimental data available in the literature.