Coherent Structures and the Generalized Lagrangian Mean Equation

Abstract

The Generalized Lagrangian mean equations are used to derive evolution equations for the perturbation flow about a turbulent mean base flow which is homogeneous in the streamwise and spanwise directions. The equations expose the mechanism which leads to the formation of streamwise vortices in the wall region of turbulent bounded flows and may be solved numerically. The advantage of this formulation is that the form of the coupling terms in the equations is known precisely; moreover, they can be expressed in terms of space time correlations, most of which have been measured. The result is a set of partial differential equations for the rectified flow field with the fluctuations filtered out. The rectified flow field then provides a way to represent the underlying coherent structures in the flow. It also permits the determination of their dynamics, which may be chaotic.