Dynamics of wall bounded flow

Abstract

There are various scenarios proposed in literature for transition in plane channel (Poiseuille) flow. In this work, one of these scenarios, namely, streak break-down, is tested numerically using a Karhunen-Loeve (K-L) based model. The K-L basis was empirically generated earlier using a numerical database representing the flow. This basis is modified in this work to include the mean flow. A K-L basis provides an optimal parametrization of the underlying flow in energy norm. Since it is specific to the flow, each basis element carries an independent characteristic of the flow and has physical interpretation. A system of model amplitude equations is then obtained by Galerkin projection of the governing equations onto the space spanned by the K-L basis. The physical interpretation of the basis elements is used to truncate the resulting system to obtain a low dimensional model.