DYNAMICS OF SPATIALLY PERIODIC FLOWS

空间周期性流动的动力学

基本信息

批准号：
05650066
负责人：
MURAKAMI Youichi
金额：
$ 0.7万
依托单位：
UNIVERSITY OF OSAKA PREFECTURE
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1994
项目状态：
已结题

项目摘要

(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.)

（a）发现具有负涡流粘度效应的大尺度模式或周期性与主光泽相同的周期性模式，给出了矩形细胞流的critil线性雷诺数。 Tabelin等人（1990年）在实验中观察到的涡流合并通过在主流量上的周期模式的叠加来定性地解释。（Phys.Fluids，第7卷（第2卷），PP-302-306（1995）。）截断的Nolinear Ode系统被得出，以表明超临界状态中存在稳定的二次流。（RIMS 1995.1。）（b）与平行流相反，由于三维干扰引起的主要不稳定性可能发生在未列表的流动中。我们已经提出了明确的例子，即临界雷诺数实际上是由三维干扰决定的。矩形细胞流（出现在plys.rev.e（1995）中），三角形范围属于这些情况。（c）在准二维流的非线性稳定性上。薄层中底部摩擦的效果大约被视为与两段ns方程中水平速度成正比的瑞利摩擦。此过程通常称为准二维近似。我们已经表明，通过线性稳定性以及通过能量方法的非线性稳定性的临界雷诺数随着雷利摩擦的增加而线性增加。（美国纽约州IUTAM专题讨论会，1993年7月26日至31日。