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

Konstantin Ilin; Andrey Morgulis

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

Mathematics

Research output: Working paper › Preprint

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.

Original language	English
Publisher	Arxiv (Cornell University)
Number of pages	20
Publication status	Published - 9 Oct 2019

Access to Document

https://arxiv.org/abs/1811.10043

Cite this

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title = "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. ",

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T1 - On the stability of the Couette-Taylor flow between rotating porous cylinders with radial flow

AU - Ilin, Konstantin

AU - Morgulis, Andrey

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N2 - 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.

AB - 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.

M3 - Preprint

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

PB - Arxiv (Cornell University)

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