Stability of Taylor-Couette and Dean flow: A semi-analytical study

An alternative method is presented for solving the eigenvalue problem that governs the stability of Taylor-Couette 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 Taylor-Couette 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. (C) 2012 Elsevier Inc. All rights reserved.