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可以给出矩形胞流的临界线性雷诺数。Tabelin et al（1990）在实验中观察到的涡旋合并用周期模态在主流上的叠加定性解释。(理论物理。液体,第七卷(没有。2)、pp - 302 - 306(1995))。导出了截断的非线性ODE系统，证明了在超临界状态下存在稳定的二次流。(轮圈1995.1。)(b)与平行流动相比，非平行流动可能发生由三维扰动引起的主要失稳。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。矩形单元流动（将出现在Plys.Rev中）。E(1995))和具有一定参数范围的三角形都属于这些情况。(c)准二维流动的非线性稳定性。在二维NS方程中，薄层底部摩擦的影响近似地视为与水平速度成比例的瑞利摩擦。这个过程通常被称为准二维近似。我们已经证明了线性稳定性计算的临界雷诺数和能量法计算的非线性稳定性计算的临界雷诺数随瑞利摩擦系数的增加而线性增加。1993年7月26日至31日，美国纽约州波茨坦。在准备。)

(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.)