Effect of Lateral Boundaries on Large-scale Mode : Linear Stability of Square Cell Flows in Rectangular Regions

概要

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Linear stability of the square cell flow represented by the stream function: F = sin x sin y isinvestigated numerically in various bounded region D : [0, Mm3 x [0, NmJ. The disturbances arelimited to two-dirnensional ones and a perfect slip condition is assumed to be applied. Specialattention is paid to clarify how the critical long-wave mode (or large-scale mode) of the flowin unbounded region is modified by lateral boundaries. It is shown that the critical rnodes areclassified into three cases according to the configuration (A#,N): (i) M = 1, (11) (M,N) =(2, odd nurnbers), (3,4) and (3,5), and (iii) the others. The last one is the most typical casesand is related to the long-wave mode in the unbounded region. The structure of the mode isone stationary vortex with the systexn size, which we call global rotation, for M x N while it isa series of stationary counter-rotating vortices for M< N . In case (11) the critical modes areoscillatory though they are related to case (iii). In case (i) (linear array of vortices) the modealso shows the global rotation, but it is rtot related to the long-wave unode in the unboundedregion.
1996-06-15