DYNAMICS OF SPATIALLY PERIODIC FLOWS

(a)结果表明，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胞流的临界线性雷诺数。Tabelin等人（1990）在实验中观察到的旋涡合并，用主流上周期性模态的叠加定性地解释了。（Phys.Fluids，第7卷（第2期），第302-306页（1995））。截断的非线性常微分方程组的推导表明，一个稳定的二次流存在于超临界状态。(RIMS 1995.1.）(b)与平行流相比，非平行流中可能发生由三维扰动引起的主要不稳定性。我们已经给出了明确的例子，临界雷诺数实际上是由三维扰动。矩形胞流（将出现在Plys.Rev.E（1995）中）和具有某些参数范围的三角形胞流属于这些情况。(c)准二维流动的非线性稳定性。在二维NS方程中，薄层底摩阻力的影响近似为与水平速度成正比的Rayleigh摩阻力。这个过程通常被称为准二维近似。我们已经表明，临界雷诺数的线性稳定性，以及非线性稳定性的能量方法增加线性的瑞利摩擦系数。（IUTAM研讨会波茨坦，纽约，美国7月26-31.1993.in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.)