Dynamical properties of forced shear layers in an annular geometry

Results of numerical simulations of a forced shear flow in an annular geome try are presented. The particular geometry used in this work reduces the ef fects of centrifugal and Coriolis forces. However, there are still a large number of system parameters (shear width, shear profile, radius of curvatur e, initial conditions, etc.) to characterize. This set of variables is limi ted after the code has been validated with experimental results (Rabaud & C ouder 1983; Chomaz et al. 1988) and with the associated linear stability an alysis. As part of the linear stability characterization, the pseudo-spectr um for the associated Orr-Sommerfeld operator for plane, circular Couette f low is calculated, and it is found to be insensitive to perturbations. The numerical simulation code is a highly accurate de-aliased spectral meth od which utilizes banded operators to increase the computational efficiency . Viscous dissipation terms enter the code directly from the equations of m otion. The results from the simulation code at low Reynolds numbers are com pared with the results from linear stability analysis and are used to give predictions for the coefficients of the Landau equation describing the satu ration behaviour near the critical Reynolds number. Numerical results at hi gher Reynolds numbers demonstrate the effects of spin-up and spin-down, inc luding the experimentally observed hysteresis. The properties of two-dimens ional shears at high Reynolds numbers, at which temporal states are formed, are also addressed.