Generation of Mean Flows by the Interaction of Goertler Vortices and Tollmien-Schlichting Waves in Curved Channel Flows.

摘要

There are many fluid flows where the onset of transition can be caused by different instability mechanisms which compete in the nonlinear regime. The interaction of a centrifugal instability mechanism with the viscous mechanism which causes Tollmein-Schlichting waves is discussed. The interaction between these modes can be strong enough to drive the mean state; the interaction is investigated in the context of curved channel flows so as to avoid difficulties associated with boundary layer growth. Essentially it was found that the mean state adjusts itself so that any modes present are neutrally stable even at finite amplitude. In the first instance, the mean state driven by a vortex of short wavelength in the absence of Tollmein-Schlichting waves is considered. It is shown that for a given channel curvature and vortex wavelength, there is an upper limit to the mass flow rate which the channel can support as the pressure gradient is increased. When the Tollmein-Schlichting waves are present, then the nonlinear differential equation to determine the mean state is modified.