DYNAMICS OF SPATIALLY PERIODIC FLOWS

空间周期性流动的动力学

• 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
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05650066/
• 关键词: linear stability; nonlinear stability; three-dimensional instability; secondary flow; vortex merging; periodic flow; cell flow; bifurcation; 流れの遷移; 空間周期流; セル構造の流れ; フロケ系; 流体力学的安定性; 非平行流安定性; 臨界レイノルズ数

(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)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www.example.com准备。）

项目成果

K.Gotoh, Y.Murakami and M.Murakami: "Instability of spatially periodic flow to three-dimensional disturbances" Fluid Dynamics Res.12. 271-279 (1993)

K.Gotoh、Y.Murakami 和 M.Murakami：“空间周期流对三维扰动的不稳定性”流体动力学 Res.12。

K.Gotoh: "Large-scale and periodic modes in rectangular cell flow" Phys.Fluids. 7. 302-306 (1995)

K.Gotoh：“矩形细胞流中的大规模和周期性模式”Phys.Fluids。

後藤金英: "Instability of spatially period ic flow to the three-dimensional distu rbances" Fluid Dynamics Research. 12. 271-279 (1993)

Kinhide Goto：“空间周期流的不稳定性对三维扰动的影响”流体动力学研究 12. 271-279 (1993)。

Y.MURAKAMI: "Unstable Modes of the Inviscid Kolmogorov Flow" J.Phys.Soc.Jpn.63. 2825-2826 (1994)

Y.MURAKAMI：“无粘柯尔莫哥洛夫流的不稳定模式”J.Phys.Soc.Jpn.63。

Y.Murakami, H.Fukuta and K.Gotoh: "Nonlinear stability of the Kolmogorov flow with the the bottom-friction using the energy method" RIMS Publication. 852. 52-66 (1993)

Y.Murakami、H.Fukuta 和 K.Gotoh：“使用能量法实现具有底部摩擦的柯尔莫哥洛夫流的非线性稳定性”RIMS 出版物。