Stability of TayloraCouette and Dean flow: A semi-analytical study

An alternative method is presented for solving the eigenvalue problem that governs the stability of TayloraCouette and Dean flow. The eigenvalue problems defined by the two-point boundary value problems are converted into initial value problems by applying unit disturbance method developed by Harris...

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Bibliographic Details
Published inApplied mathematical modelling Vol. 37; no. 4; pp. 1627 - 1637
Main Authors Deka, R K, Paul, A
Format Journal Article
LanguageEnglish
Published 15.02.2013
Subjects
Computation
Disturbances
Eigenvalues
Initial value problems
Mathematical analysis
Mathematical models
Stability
Wavelengths
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Summary:An alternative method is presented for solving the eigenvalue problem that governs the stability of TayloraCouette and Dean flow. The eigenvalue problems defined by the two-point boundary value problems are converted into initial value problems by applying unit disturbance method developed by Harris and Reid [27] in 1964. Thereafter, the initial value problems are solved by differential transform method in series and the eigenvalues are computed by shooting technique. Critical wave number and Taylor number for TayloraCouette flow are computed for a wide range of rotation ratio ( mu ), -4 <= mu <= 1 (first mode) and -2 <= mu <= 1 (second mode). The radial eigenfunction and cell patterns are presented for mu = -1, 0, 1. Also, we have computed critical wave number and Dean number successfully.
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ISSN:0307-904X
DOI:10.1016/j.apm.2012.04.025