Flow regimes in a simplified Taylor–Couette-type flow model

Abstract

In this paper we introduce a simplified variant of the well-known Taylor-Couette flow.The aim is to develop and investigate a model problem which is as simple as possible while admitting a wide range of behaviour, and which can be used for further study into stability, transition and ultimately control of flow. As opposed to models based on ordinary differential equations, this model is fully specified by a set of partial differential equations that describe the evolution of the three velocity components over two spatial dimensions, in one meridian plane between the two counter-rotating coaxial cylinders.We assume axisymmetric perturbations of the flow in a narrow gap limit of the governing equations and, considering the evolution of the flow in a narrow strip of fluid between the two cylinders, we assume periodic boundary conditions along the radial and axial directions, with special additional symmetry constraints. In the paper, we present linear stability analysis of the first bifurcation, leading to the well known Taylor vortices, and of the secondary bifurcation, which, depending on the type of symmetries imposed on the solution, can lead to wave-like solutions travelling along the axial direction. In addition, we show results of numerical simulations to highlight the wide range of flow structures that emerge, from simple uni-directional flow to chaotic motion, even with the restriction placed on the flow.

A framework for input–output analysis of wall-bounded shear flows

“…The Poincaré constant is then given by C = π 2 √ L 2 +2 2 . The linear stability limit of the flow can be computed by studying the spectrum of the linearized model (Lasagna et al (2016)). That is,…”

“…We consider the flow between two co-axial cylinders, where the gap between the cylinders is much smaller than their radii. In this setting, the flow can be represented by the Couette flow subject to rotation (Lasagna et al (2016)) as illustrated in Figure 10. The axis of rotation is parallel to the x 3 -axis and the circumferential direction corresponds u(y, z) to x 1 -axis.…”

Transient generalized Taylor-Couette flow: a semi-analytical approach

“…They opined that the energy gradient method which is a semi-empirical theory is effectual for rotating fluid flows. Stability and instability of Taylor-Couette flow and Couette flow analysis have been investigated thoroughly numerically and experimentally over the past years found in [3][4][5][6][7][8][9]. Hristova et al [10] stated that transient growth is enhanced by the curvature of the rotating cylinders [11].…”