Instability of a two-dimensional viscous flow in an annulus with permeable walls to two-dimensional perturbations
Instability of a two-dimensional viscous flow in an annulus with permeable walls to two-dimensional perturbations
复制标题
具有渗透壁的环形空间中二维粘性流对二维扰动的不稳定性
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
A. Morgulis
中科院分区：
文献类型：
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作者：
K. Ilin;A. Morgulis
本文研究了具有可渗透壁的环形空间中二维粘性流动在二维小扰动下的稳定性。基本定常流是Navier-Stokes方程的最一般的旋转不变解，其中速度具有径向和方位角分量，并且方位角速度分布取决于径向雷诺数。结果表明，对于宽范围的参数的问题，基本流是不稳定的小的二维扰动。计算了问题参数空间中的中性曲线。计算表明，当径向流方向由内向外时，该流动的稳定性由内筒处的方位角速度决定;当径向流方向相反时，该流动的稳定性由外筒处的方位角速度决定。本文工作是我们以前对旋转多孔圆柱间流动无粘不稳定性研究的继续[K。Ilin和A. Morgulis，“Instability of an Inviscid Flow between porous cylinders with radial flow，”J. Fluid Mech.730，364-378（2013）]。
The stability of a two-dimensional viscous flow in an annulus with permeable walls with respect to small two-dimensional perturbations is studied. The basic steady flow is the most general rotationally invariant solution of the Navier-Stokes equations in which the velocity has both radial and azimuthal components, and the azimuthal velocity profile depends on the radial Reynolds number. It is shown that for a wide range of parameters of the problem, the basic flow is unstable to small two-dimensional perturbations. Neutral curves in the space of parameters of the problem are computed. Calculations show that the stability properties of this flow are determined by the azimuthal velocity at the inner cylinder when the direction of the radial flow is from the inner cylinder to the outer one and by the azimuthal velocity at the outer cylinder when the direction of the radial flow is reversed. This work is a continuation of our previous study of an inviscid instability in flows between rotating porous cylinders [K. Ilin and A. Morgulis, “Instability of an inviscid flow between porous cylinders with radial flow,” J. Fluid Mech. 730, 364–378 (2013)].