Title: Low-dimensional modeling for temporally developing free shear layers

Speaker: Mingjun Wei, Assistant Professor, Mechanical Engineering Dept., New Mexico State University

Date/Time: Monday, October 29, 2007, 1:00 pm – 2:00 pm

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: We develop low-dimensional models for the evolution of a free shear layer in a periodic domain. The goal is to obtain models simple enough to be analyzed using standard tools from dynamical systems theory, yet including enough of the physics to model nonlinear saturation and energy transfer between modes (e.g., pairing). Low- dimensional models for these dynamics are obtained using a modified version of proper orthogonal decomposition/Galerkin projection, in which the basis functions can scale in space as the shear layer spreads. Equations are obtained for the rate of change of the shear layer thickness. A model with 2 complex modes can describe certain single-frequency features of the system, such as vortex roll-up, nonlinear saturation, and viscous damping. A 4-mode model can describe interactions between two frequencies (vortex merging) as well. It is indicated that for each frequency at least two POD modes with opposite symmetric behavior are needed to describe the dynamics properly. The incompressibility of each modes is enforced during the scaling, and this turns out to be important in successful modeling.