Secondary vortices in turbulent square duct flow

Description

A linear approach, inspired by hydrodynamic stability theory, is used to describe the presence of large scale coherent vortices for the turbulent flow in a duct of square crosssection. A set of equations for the small-amplitude coherent motion is derived and closed with a simple mixing length strategy. The initial condition that maximizes a chosen functional (related to either the kinetic energy of the coherent motion or the rate of turbulence production) is found through a direct/adjoint numerical approach borrowed from optimal control theory. It is found that different kinds of secondary flows can appear in the duct cross-section, sustained by the mean shear. Some of these optimal states display a symmetry about the bisectors and the diagonals of the duct, in agreement to experimental observations and direct numerical simulations. © 2005 by A. Bottaro, H. Soueid and B. Galletti.

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