A note on the onset of recirculation in a 2D Couette flow over a wavy bottom
A note on the onset of recirculation in a 2D Couette flow over a wavy bottom
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关于波状底部的 2D Couette 流中再循环开始的注释
DOI：
10.1063/1.4906153
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发表时间：
2015
影响因子：
4.6
通讯作者：
P. Salles
中科院分区：
文献类型：
--
作者：
F. M. Esquivelzeta;B. Figueroa‐Espinoza;D. Legendre;P. Salles
在二维周期性数值域中，采用直接数值模拟方法研究了固定波纹表面上的层流Couette流动。网格是通过保角变换生成的，保角变换将水平流设置在域的顶部，其中给定恒定速度边界条件。域的底部是波斜率为2πa/λ的波状正弦曲面。采用不同的雷诺数（Re）和两个无量纲参数（通道宽度h、波长λ和波浪形底部振幅a），研究了底部形状、惯性和粘度的综合影响。即使雷诺数很大，模拟也不会受到扰动，因此状态始终是层流。然而，在低压槽附近出现了再循环。涡心的水平位置是2πa/λ和Reλ/h的函数。这种再循环的发病条件进行了研究，并与文献中的结果进行了比较。从数值结果中可以清楚地识别出两个区域：粘性区域，在小雷诺数时，在2πa/λ和Reλ/h之间具有弱相关性;惯性区域，在大雷诺数时，在2πa/λ和Reλ/h之间具有指数相关性，其近似斜率为−1/3。几乎所有的结果都包含在一条表征该现象的曲线中（除了由于大λ/h比而限制流动的某些点）。
Laminar Couette flow over a fixed wavy surface was studied with direct numerical simulation in a 2D periodic numerical domain. The mesh was generated by a conformal transformation that sets horizontal flow at the top of the domain, where a constant velocity boundary condition is given. The bottom of the domain is a wavy sinusoidal surface of wave slope 2πa/λ. The combined effect of bottom shape, inertia, and viscosity was explored using different Reynolds numbers (Re) and two dimensionless parameters in terms of channel width h, wavelength λ, and the amplitude of the wavy bottom a. Even if the Reynolds number was large, the simulations were not perturbed so the regime was always laminar. However, a recirculation appeared at the vicinity of the trough. The horizontal location of the eddy center was reported as a function of 2πa/λ and Reλ/h. The conditions for the onset of this recirculation were studied and compared with results from the literature. Two regimes can be clearly identified from the numerical results; a viscous regime with a weak dependence between 2πa/λ and Reλ/h for small Reynolds numbers and an inertial regime with an exponential dependence between 2πa/λ and Reλ/h for large Reynolds numbers, which presents an approximate slope of −1/3. Almost all results collapse in one single curve that characterizes the phenomenon (with the exception of some points where the flow is confined due to a large λ/h ratio).