Research Institute for mathematical Sciences, Kyoto University, Kyoto 606, Japan
Department of Physics, Faculty of Science, Kyoto University, Kyoto 606, Japan
Abstract:
Instability of two-dimensional periodic flows with rhombic cell structure represented by the stream function Ψ=cos kx+cosy is investigated. Stability characteristics are obtained for the Reynolds number R=1, 2, 3 and 4 and the ratio of the diagonals of the cell
. Variation of the critical Reynolds number Rc with k is obtained, and the square cell flow (k=1) is found to be most stable (Rc=√2). It is found that Rc → 1 as k → 0, which leads to a finite gap between this limiting Rc and Rc=√2 for K=0 (Ψ=cos y).