Nonlinear stability characteristics of rotating plane channel Poiseuille flow with the outcome of nonlinear evolution equation

Abstract

This paper considers the laminar to turbulent transition of pressure-gradient driven Poiseuille flow in a plane channel system rotating with some angular speed under the influence of the Coriolis force. The nonlinearities are taken into account in the fundamental equations of motion for the perturbations grown enough to cause laminar to turbulent transition in rotating channel flow. For the values of Reynolds number slightly greater than the critical values above which the perturbations may grow, the time and length scales are chosen for the slow variations in the amplitude parameter B of a nonlinear two-dimensional perturbation wave in plane channel flow rotating as a whole. By the method of multiple scales, the nonlinear complex evolution equation, called here the Ginzburg–Landau–Stewartson–Stuart equation, is derived for scalar function B dependent on slow and long scale variables of both time and space. The coefficients of this equation are calculated analytically and computationally, which contain all the parameters causing laminar to turbulent transition along with the departure parameter from the neutral stable surface toward the growing side. The laminar to turbulent transition can be analyzed by the solution of this nonlinear equation, which is dependent on its coefficients containing the non-dimensional flow parameters.