Low Order Representations in the Turbulent Wake of a Normal Flat Plate

Abstract

The turbulent wake of a normal flat plate, characterized by quasi-periodic vortex-shedding dynamics, is investigated in the context of low-order modeling, non-linear dynamics and kinetic energy transfer. The flow is characterized, coherent-structures are educed through the implementation of three models, and the transfer of kinetic energy between the most energetic structures and to the unresolved scales of motion is investigated. A low-order kinematic model (LOM) is constructed via the truncation of a Galerkin expansion using the energetically-optimal proper orthogonal decomposition (POD). The harmonic and shift modes of the LOM are coupled via the mean-field paraboloid in phase space, enabling the construction of a generalized phase-average (GPA). The GPA is shown to capture key flow behaviour and physics that traditional phase-averaging (TPA) cannot, including variation in the base flow and modulation of the vortex-shedding amplitude. A clearer understanding of energy transfer is made possible through the simplified representations of the models.