Institute of Science and Technology Austria (IST Austria), 3400 Klosterneuburg, Austria.
Department of Mechanical Engineering and Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, USA.
Phys Rev E. 2017 May;95(5-1):053103. doi: 10.1103/PhysRevE.95.053103. Epub 2017 May 10.
We present a numerical study of wavy supercritical cylindrical Couette flow between counter-rotating cylinders in which the wavy pattern propagates either prograde with the inner cylinder or retrograde opposite the rotation of the inner cylinder. The wave propagation reversals from prograde to retrograde and vice versa occur at distinct values of the inner cylinder Reynolds number when the associated frequency of the wavy instability vanishes. The reversal occurs for both twofold and threefold symmetric wavy vortices. Moreover, the wave propagation reversal only occurs for sufficiently strong counter-rotation. The flow pattern reversal appears to be intrinsic in the system as either periodic boundary conditions or fixed end wall boundary conditions for different system sizes always result in the wave propagation reversal. We present a detailed bifurcation sequence and parameter space diagram with respect to retrograde behavior of wavy flows. The retrograde propagation of the instability occurs when the inner Reynolds number is about two times the outer Reynolds number. The mechanism for the retrograde propagation is associated with the inviscidly unstable region near the inner cylinder and the direction of the global average azimuthal velocity. Flow dynamics, spatio-temporal behavior, global mean angular velocity, and torque of the flow with the wavy pattern are explored.
我们呈现了一个数值研究，探讨了在两个反向旋转的圆柱之间的超临界波浪形圆柱 Couette 流动中，波状图案是如何向前行（与内圆柱同向）还是逆行（与内圆柱的旋转方向相反）传播的。当波不稳定性的相关频率消失时，内圆柱雷诺数的特定值会导致波的传播从前行到逆行，反之亦然。这种反转发生在两倍和三倍对称的波浪涡旋中。此外，只有当反向旋转足够强时，波的传播才会发生反转。由于不同系统尺寸的周期性边界条件或固定端壁边界条件总是导致波的传播反转，因此这种流动模式的反转似乎是系统固有的。我们提出了一个详细的分岔序列和参数空间图，展示了波浪流动的逆行行为。当内圆柱雷诺数大约是外圆柱雷诺数的两倍时，不稳定性就会逆行传播。逆行传播的机制与内圆柱附近的无粘不稳定区域以及全局平均角向速度的方向有关。我们还研究了具有波浪图案的流动的动力学、时空行为、全局平均角速度和扭矩。
