NONLINEAR CONVECTION IN A ROTATING LAYER WITH FINITE CONDUCTING BOUNDARIES

Small-amplitude steady thermal convection is a horizontal layer of fluid with finite conducting boundaries and rotating about a vertical axis is investigated. Both analytical and numerical techniques are used to solve the nonlinear and stability problems. Conditions on the parameters γb, γt, and τ are determined under which either square cells or two-dimensional rolls can be the preferred form of convection (γb and γt are the ratios of the thermal conductivities of the lower and upper boundaries to that of the fluid and τ is the rotation parameter). Transition from steady rolls to time-dependent flow occurs for τ beyond some value, which decreases with decreasing γb or γt. Square cell convection is not subject to such transition, but there is a transition from steady squares to steady rolls for τ beyond a critical value. The dependence on γb, γt, and τ of the time-dependent transition and of the heat transported by convection are also discussed. © 1990 American Institute of Physics.