The structure of highly nonlinear vortices in curved channel flow

The structure of highly nonlinear, small wavelength Gortler vortices is analysed for fully developed flow in a curved channel. The Taylor number is taken to be <i>T</i>₀ε^-5 , which is asymptotically larger than the neutral stability Taylor number for vortices of small wavelength 2πε. Over most of the flow domain the motion is determined by the interaction of the mean flow and terms proportional to exp {iz/ε}, whereas adjacent to the outer channel wall there is a boundary layer of thickness <i>O</i>(ε) which requires all the harmonics of the disturbance to be considered. Numerical solutions of the wall layer equations are presented for T₀ up to 14000 with the main feature of these results being the development of a weak vortex on the boundary layer lengthscale.