Linear stability characteristics of the pressure-gradient driven flow confined in concentric cylinders with the rotation of outer cylinder and translation of inner cylinder

In this contribution laminar to turbulent transition is studied in a pressure gradient driven flow confined between Taylor cylinders. The outer cylinder is assumed rotating and the inner cylinder is under translational motion. In this respect, a mathematical model describing the physics of flow dynamics is presented and implemented using MATLAB. Spectral collocation approach is used to calculate the eigenvalues which predict the critical stability parameter value. The critical parameters at which the laminar to turbulent transition just starts are calculated. The neutral stability diagrams are obtained for various physical situations characterizing the limit points of damping and growth of the wave disturbances. It is observed that an increase in the swirl and translation allows the transition to start later than the classical case. However, increase in the gap width allows the transition to appear earlier than the classical case. A change in the Tollmien Schlichting mechanism is seen with the change in swirl, translation and gap width of the two cylinders. Moreover, the linear stability analysis discussed here provides a basis for the nonlinear stability analysis with the help of adjoints calculated and presented.