Linear stability of the rectangular cell flow: PSgr;=costhinsp;kxthinsp;costhinsp;y(0k1), is studied, both numerically and analytically. Owing to its spatial periodicity, the disturbances are characterized by the Floquet exponents (agr;,bgr;). Based on numerical results, it is found that two types of the critical modes with vanishingly small exponents exist. One type (largehyphen;scalemode) has an almost uniform spatial structure. The other type (periodicmode) has a structure with the same periodicity as the main flow. The largehyphen;scale mode gives the critical Reynolds number in a more isotropic case (i.e.,kgsim;0.6), while the periodic mode does so in the less isotropic case (i.e.,k0.6). Asymptotic expansions from (agr;,bgr;)=(0,0) agree with the numerical results. Using the periodic mode, a possible explanation is given for the merging process of a pair of counterhyphen;rotating vortices observed in the experiments of a linear array of vortices by Tabelingetal. lsqb;J. Fluid Mech.213, 511 (1990)rsqb;. copy;1995 American Institute of Physics.
展开▼
