Results of numerical simulations of a forced shear flow in an annular geometry are presented. The particular geometry used in this work reduces the effects of centrifugal and Coriolis forces. However, there are still a large number of system parameters (shear width, shear profile, radius of curvature, initial conditions, etc.) to characterize. This set of variables is limited after the code has been validated with experimental results (Rabaud & Couder 1983; Chomaz et al. 1988) and with the associated linear stability analysis. As part of the linear stability characterization, the pseudo-spectrum for the associated Orr-Sommerfeld operator for plane, circular Couette flow is calculated, and it is found to be insensitive to perturbations. The numerical simulation code is a highly accurate de-aliased spectral method which utilizes banded operators to increase the computational efficiency. Viscous dissipation terms enter the code directly from the equations of motion. The results from the simulation code at low Reynolds numbers are compared with the results from linear stability analysis and are used to give predictions for the coefficients of the Landau equation describing the saturation behaviour near the critical Reynolds number. Numerical results at higher Reynolds numbers demonstrate the effects of spin-up and spin-down, including the experimentally observed hysteresis. The properties of two dimensional shears at high Reynolds numbers, at which temporal states are formed, are also addressed.
Cambridge University Press
Journal of Fluid Mechanics
Journal of Fluid Mechanics, 402: 255-289