Transition to oscillatory motion in rotating channel flow

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Abstract
A numerical study of the transition from steady to oscillatory streamwise-oriented vortices in fully developed rotating channel flow is presented. The principal results are obtained from three-dimensional, spectral simulations of the incompressible time-dependent Navier–Stokes equations. With increasing Reynolds number, two transitions that cause the steady, periodic array of two-dimensional vortices (roll cells) to develop waves travelling in the streamwise direction are discovered. The linear stability of two-dimensional vortices to wavy perturbations is examined. Associated with the two transitions are two different wavy vortex flows: WVF1 and WVF2. WVF2 is very similar to undulating vortex flow found in curved channel flow simulations (Finlay, Keller & Ferziger 1988) and to wavy Taylor vortex flow. WVF2 is only possible at low rotation rates. In contrast, the dissimilar WVF1 occurs for all rotation rates examined, has shorter streamwise wavelength and, for sufficiently high Reynolds number, has much higher linear growth rate than WVF2. For low rotation rates, WVF1 is similar to curved channel flow twisting vortices, but at higher rotation rates appears dissimilar. Several key qualitative features are discussed that suffice in describing all these wavy vortex flows.
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