%0 Journal Article
%T Exact coherent structures in a reduced model of parallel shear flow
%A Cedric Beaume
%A Edgar Knobloch
%A Greg P. Chini
%A Keith Julien
%J Physics
%D 2014
%I arXiv
%X A reduced description of shear flows consistent with the Reynolds number scaling of lower-branch exact coherent states in plane Couette flow [J. Wang et al., Phys. Rev. Lett. 98, 204501 (2007)] is constructed. Exact time-independent nonlinear solutions of the reduced equations corresponding to both lower and upper branch states are found for Waleffe flow [F. Waleffe, Phys. Fluids 9, 883--900 (1997)]. The lower branch solution is characterized by fluctuations that vary slowly along the critical layer while the upper branch solutions display a bimodal structure and are more strongly focused on the critical layer. The reduced model provides a rational framework for investigations of subcritical spatiotemporal patterns in parallel shear flows.
%U http://arxiv.org/abs/1402.4123v1