Abstract
In a natural circular loop, the thermal convection demonstrates various spatial patterns and temporal instabilities. Problem consists in determining them with respects to thermal boundary conditions. To this end a multiple scales analysis is applied which resembles the inherent characteristic of the pattern formation in the Rayleigh-Be´nard convection. A three-dimensional nonlinear model is proposed by incorporating the flow modes derived along the analysis. The differences of thermal boundary condition are reflected by a coefficient δ. For small δ, numerical solution to the model shows that only temporal instability exists and Lorenz chaos is possible, otherwise, for large values both spatial and temporal instabilities occur leading to cellular flow and intermittency chaos. The model predicted some additional phenomena opening for experimental observation. It seems significant that this study proposes an algorithm for the control of flow stability and distribution by varying the thermal boundary condition.
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