Modal energy flow analysis of a highly modulated wake behind a wall-mounted pyramid

摘要

We experimentally investigate the highly modulated turbulent wake behind a wall-mounted square-base pyramid protruding through the boundary layer. We present the first modal energy flow analysis of a time-resolved three-dimensional velocity field from experimental particle image velocimetry data. The underlying low-order representation is optimized for resolving the base-flow variation as well. as the first and second harmonics associated with vortex shedding generalizing the triple decomposition of Reynolds & Hussain (J Fluid Mech., vol. 54, 1972, pp. 263-288). This analysis comprises not only a detailed modal balance of turbulent kinetic energy as pioneered by Rempfer & Fasel tJ, Fluid Mech.., vol. 275, 1994, pp. 257-283) for proper orthogonal decomposition (POD) models, but also the companion energy balance of the mean flow. The experimental results vividly demonstrate how constitutive elements of mean-field theory (Stuart, J. Fluid Mech., vol. 4, 1958, pp. 1-21) near laminar llopf bifurcations remain strongly pronounced in a turbulent wake characterized by highly modulated, quasi-periodic shedding. The study emphasizes, for instance, the stabilizing role of mean-field manifolds, as explored in the pioneering POD model of Aubry et al. (I. Fluid Mech., vol. 192, 1988, pp. 115-173). 'file presented low-order representation of the flow and modal energy flow analyses may provide important insights and reference data for computational turbulence modelling, e.g. unsteady Reynolds-averaged Navier Stokes simulations.