On the stability of the Couette–Taylor flow between rotating porous cylinders with radial flow

Abstract

We study the stability of the Couette-Taylor flow between porous cylinders with radial throughflow. It had been shown earlier that this flow can be unstable with respect to non-axisymmetric (azimuthal or helical) waves provided that the radial Reynolds number, R (constructed using the radial velocity at the inner cylinder and its radius), is high. In this paper, we present a very detailed and, in many respects, novel chart of critical curves in a region of moderate values of R, and we show that, starting from values of R, as low as 10, the critical modes inherited from the inviscid instability gradually substitute the classical Taylor vortices. Also, we have looked more closely at the effect of a weak radial flow (relatively low R) on the Taylor instability and found that a radial flow directed from the inner cylinder to the outer one is capable of stabilizing the Couette-Taylor flow provided that the gap between the cylinders is wide enough. This observation is in a sharp contrast with the case of relatively narrow gaps for which the opposite effect is well-known.

Linear Stability of a Steady Convective Flow between Permeable Cylinders

“…Such models (in the presence of rotation) are motivated by applications to dynamic filtration devices and vortex flow reactors [12,13]. The stability of such flows is investigated in [14][15][16]. In the case of non-isothermal conditions, the presence of radial flow can alter the perturbation dynamics.…”

Flow dynamics between two concentric counter-rotating porous cylinders with radial through-flow

“…Ilin and Morgulis [39] found (in linear stability analysis) that for counter-rotating cylinders a destabilizing effect of a weak diverging flow can occur for all values of the gap between the cylinders, depending on gap width. They detected that a sufficiently strong increase in radial flow, directed either inward or outward, flattens the critical curves in the (Re i , Re o ) plane, which means that the stability properties of the basic flow are almost independent of Re o , i.e., the effect of the outer cylinder becomes very weak, which is in agreement with earlier results [27].…”