Effect of outer cylinder rotation on the radially heated Taylor-Couette flow

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Summary:

Taylor–Couette flow (TCF) refers to the annular flow between two concentric, differentially rotating cylinders. After Taylor’s seminal 1923 article, the topic remains an active research area even today after a centrury due to its experimental simplicity and a wide range of applications.

This work adds to the current literature on the radially heated TCF. Some key results of this paper are summarized below.

• We find unstable modes in the Rayleigh stable region of the parameter space.
• We generalize previously identified symmetries of the linear problem to the case of rotating outer cylinder.
• We locate instability islands also known as closed disconnected neutral curves (CDNCs) for a number of parameters.
• We show by example that CDNCs are sensitive to changes in the rotation rate ratio and their appearance or disappearance can induce discontinous jumps in the critical Taylor number.

Code:

The code used to generate and plot data in the paper can be downloaded from here.

Personal notes:

This paper is special to me for two principal reasons –

(i) It comes in the year 2023, the hudrenth anniversary of Taylor’s seminal 1923 article. It’s a personal hat-tip to Taylor’s inspiring work. (ii) I worked with a long time friend Mohammad Atif, currently a postdoc at the Brookhaven National Labs, NY. It was really fun working together.