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The strong nonlinear interaction of Tollmien–Schlichting waves and Taylor–Görtler vortices in curved channel flow

Viscous fluid flows with curved streamlines can support both centrifugal and viscous travelling wave instabilities. Here the interaction of these instabilities in the context of the fully developed flow in a curved channel is discussed. The viscous (Tollmien–Schlichting) instability is described asymptotically at high Reynolds numbers and it is found that it can induce a Taylor–Görtler flow even at extremely small amplitudes. In this interaction, the Tollmien–Schlichting wave can drive a vortex state with wavelength either comparable with the channel width or the wavelength of lower-branch viscous modes. The nonlinear equations which describe these interactions are solved for nonlinear equilibrium states.