DYNAMICS OF SPATIALLY PERIODIC FLOWS

(a)发现具有负涡粘效应的大尺度模态或与主辉光周期相同的周期模态给出了矩形单元流的临界线性雷诺数。 Tabelin 等人（1990）在实验中观察到的涡合并通过主流上的周期模式的叠加来定性地解释。 (Phys.Fluids, Vol.7(No.2), pp-302-306(1995).) 导出截断非线性 ODE 系统以表明超临界状态下存在稳定的二次流。 (RIMS 1995.1.)(b) 与平行流相比，非平行流中可能会出现由三维扰动引起的主要不稳定。我们已经给出了明确的例子，表明临界雷诺数实际上是由三维扰动决定的。矩形单元流(出现在Plys.Rev.E(1995)中)和具有一定参数范围的三角形单元流就属于这些情况。(c)关于准二维流的非线性稳定性。薄层中底部摩擦力的影响近似视为二维NS方程中与水平速度成正比的瑞利摩擦力。该过程通常称为准二维近似。我们已经证明，线性稳定性的临界雷诺数以及能量法的非线性稳定性随着瑞利摩擦系数的增加而线性增加。 （IUTAM 研讨会，美国纽约州波茨坦，1993 年 7 月 26-31 日，筹备中。）

(a) It is found that the large-scale mode with the negative eddy viscosity effect or the periodic mode whose periodicity is the same as the main glow gives the critil linear Reynolds number of the rectangular cell flow. The vortex merging which was observed in the experiments by Tabelin et al (1990) is explained qualitatively by superposition of the periodic mode on the main flow. (Phys.Fluids, Vol.7(No.2), pp-302-306(1995).) The truncated nolinear ODE system is derived to show that a steady secondary flow exists in the supercritical regime. (RIMS 1995.1.)(b) In the contrast with the parallel flows, the primary instability due to the three-dimensional disturbance may take place in the non-paralled flows. We have presented explicit examples that the critical Reynolds number is actually determined by the three-dimensional disturbances. The rectangular cell flows (to appear in Plys.Rev.E(1995)) and the triangular ones with some parameter ranges belong to these cases.(c) On the nonlinear stability of the quasi-two-dimensional flows. The effect of the bottom-friction in the thin layr is approximatety regarded as the Rayleigh friction proportional to the horizontal velocity in the two-dimesional NS equation. This procedure is often called the quasi-two-dimensional approximation. We have shown that the critical Reynolds number by the linear stability as well as the nonlinear stability by the energy method increases linearly with increasing the coefficient of the Rayleigh friction. (IUTAM Symposium Potsdam, NY,USA July 26-31.1993.in preparation.)