Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA.
Department of Mechanical Engineering, FAMU-FSU College of Engineering, Tallahassee, FL 32310, USA.
Philos Trans A Math Phys Eng Sci. 2023 May;381(2246):20220136. doi: 10.1098/rsta.2022.0136. Epub 2023 Mar 13.
Taylor-Couette flow is a canonical flow to study Taylor-Görtler (TG) instability or centrifugal instability and the associated vortices. TG instability has been traditionally associated with flow over curved surfaces or geometries. In the computational study, we confirm the presence of TG-like near-wall vortical structures in two lid-driven flow systems, the Vogel-Escudier (VE) and the lid-driven cavity (LDC) flows. The VE flow is generated inside a circular cylinder by a rotating lid (top lid in the present study), while the LDC flow is generated inside a square or rectangular cavity by the linear movement of the lid. We look at the emergence of these vortical structures through reconstructed phase space diagrams and find that the TG-like vortices are seen in the chaotic regimes in both flows. In the VE flow, these vortices are seen when the side-wall boundary layer instability sets in at large [Formula: see text]. The VE flow is observed to go to a chaotic state in a sequence of events from a steady state at low [Formula: see text]. In contrast to VE flows, in the LDC flow with no curved boundaries, TG-like vortices are seen at the emergence of unsteadiness when the flow exhibits a limit cycle. The LDC flow is observed to have transitioned to chaos from the steady state through a periodic oscillatory state. Various aspect ratio cavities are examined in both flows for the presence of TG-like vortices. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal paper (Part 2)'.
泰勒-库埃特流是一种经典的流动，用于研究泰勒-戈尔特勒（TG）不稳定性或离心不稳定性以及相关的涡旋。TG 不稳定性传统上与曲面或几何形状上的流动有关。在计算研究中，我们在两种驱动盖流系统（Vogel-Escudier（VE）和驱动盖腔（LDC）流）中证实了存在类似 TG 的近壁涡结构。VE 流是由旋转盖（本研究中的顶盖）在圆柱体内产生的，而 LDC 流是由盖的线性运动在方形或矩形腔内产生的。我们通过重构相空间图来观察这些涡结构的出现，并发现这些类似 TG 的涡在两种流动的混沌状态中都可以看到。在 VE 流中，当侧壁边界层不稳定性在大[Formula: see text]时，这些涡就会出现。VE 流在[Formula: see text]较低的情况下从稳态进入一系列事件后进入混沌状态。与 VE 流不同，在没有弯曲边界的 LDC 流中，当流动表现出极限环时，会出现类似 TG 的涡。LDC 流在从稳态通过周期性振荡状态过渡到混沌状态时观察到。在两种流动中，都检查了各种纵横比的腔以观察是否存在类似 TG 的涡。本文是主题问题“泰勒-库埃特流和相关流动百年纪念（第 2 部分）”的一部分。
