Numerical experiments on time-dependent rotational Couette flow

Abstract

The flow induced by impulsively starting the inner cylinder in a Couette flow apparatus is investigated by using a nonlinear analysis. Explicit finite-difference approximations are used to solve the Navier–Stokes equations for axisymmetric flows. Random small perturbations are distributed initially and periodic boundary conditions are applied in the axial direction over a length which, in general, is chosen to be the critical wavelength observed experimentally. Simultaneous occurrence of Taylor vortices is obtained at supercritical Reynolds numbers. The development of streamlines, perturbation velocity components and the kinetic energy of the perturbations is examined in detail. Many salient features of the physical flow are observed in the numerical experiments.