Instability of the Hocking-Stewartson pulse and its implications for three-dimensional Poiseuille flow

The linear stability problem for the Rocking-Stewartson pulse, obtained by linearizing the complex Ginzburg-Landau (cGL) equation, is formulated in te rms of the Evans function, a complex analytic function whose zeros correspo nd to stability exponents. A numerical algorithm based on the compound matr ix method is developed for computing the Evans function. Using values in th e cGL equation associated with spanwise modulation of plane Poiseuille flow , we show that the Hocking-Stewartson pulse associated with points along th e neutral curve is always linearly unstable due to a real positive eigenval ue. Implications for the spanwise structure of nonlinear Poiseuille problem between parallel plates are also discussed.