Non-Stationary Finite-Amplitude Convection in a Thin Fluid Layer Bounded by a Stably Stratified Region

Abstract

Numerical integrations are performed for the equations governing two-dimensional convection flows in a fluid confined between two horizontal plates. A situation considered here is that local heating at a time-independent rate is provided at the middle level of the fluid so that the upper half of the fluid is destabilized and the lower half stabilized. It is shown that steady-state solutions are obtained when the Rayleigh number (R) is 1.1 times Rc (critical Rayleigh number at which convection sets in according to the linearized theory). For three cases where R=1.5 Rc, 2 Rc and 3 Rc, time-dependent solutions are obtained which describe extremely regular and repeatable convection flows. The flow pattern is such that plume-like cells generated by heating move horizontally, merge with neighboring plumes, and new plumes are generated. This process is repeated. Time-dependent but irregular solutions are obtained for R=5 Rc and beyond.