Large-scale vortex structures in shear flows

Abstract

This article considers the developments of the Hamiltonian Approach to problems of fluid dynamics, and applies the general method to strongly non-linear large-scale vortex structures in shear flows. Such vortex structures can appear in shear flows like Poiseulle and Couette flows. The Hamiltonian version of contour dynamics for two-dimensional layer models in a constant-density ideal fluid has be developed. The Hamiltonian description is formulated in terms of the dynamic variables with KdV-type Poisson brackets. The use of the method of pseudo-differential operators permits the regular application of approximation methods. Thus, governing equations can be easily derived correctly in any order of perturbation theory. We discuss also the effect of vortex structures on the average velocity profile of the flows.