Numerical Analysis of Oscillatory Instability of Buoyancy Convection With the Galerkin Spectral Method

The Galerkin spectral method with basis Junctions previously introduced by Gelfgat 111 is applied for analysis of oscillatory instability of convective flows in laterally heated rectangular cavities. Convection of water and air in a square cavity, and convection of a tow-Prandtl-number fluid in a square cavity, and a cavity with a ratio length / height of 4 are considered. Patterns of the most unstable perturbations of the stream function and the temperature are presented, and mechanisms of oscillatory instability are discussed. Comparison with other numerical investigations shows that the Galerkin method with divergent-free basis functions, which satisfy all the boundary conditions, needs fewer modes than other methods using discretization of the flow region.