1The emergence of localized vortex-wave interaction states in plane Couette flow

The recently understood relationship between high Reynolds number vortex-wave inter-action theory and computationally-generated self-sustaining processes provides a possible route to an understanding of some of the underlying structures of fully turbulent flows. Here vortex-wave interaction theory, which we now refer to as VWI, is used in the long streamwise wavelength limit to continue the development found at order one wavelengths by Hall and Sherwin (2010). The asymptotic description given reduces the Navier-Stokes equations to the so-called boundary-region equations for which we find equilibrium states describing the change in the VWI as the wavelength of the wave increases from O(h) to O(Rh) where R is the Reynolds number and 2h is the depth of the channel. The reduced equations do not include the streamwise pressure gradient of the perturbation or the effect of streamwise diffusion of the wave-vortex states. The solutions we calculate have an asymptotic error proportional to R−2 when compared to the full Navier-Stokes equa-tions. The results found correspond to the minimum drag configuration for VWI states and might therefore be of relevance to the control of turbulent flows. The key feature of the new states discussed here is the thickening of the critical layer structure associate