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 (μ), −4 ⩽ μ ⩽ 1 (first mode) and −2 ⩽ μ ⩽ 1 (second mode). The radial eigenfunction and cell patterns are presented for μ = −1, 0, 1. Also, we have computed critical wave number and Dean number successfully.