The spatial evolution of fluctuations in a self-propelled wake compared to a patch of turbulence

Abstract

The primary focus of this study is to contrast the influence of the mean velocity profile with that of the initial turbulence on the subsequent evolution of velocity and density fluctuations in a stratified wake. Direct numerical simulation is used to simulate the following cases: (a) a self-propelled momentumless turbulent wake, case SP50 with a canonical mean velocity profile, (b) a patch of turbulence, case TP1 with the same initial energy spectrum as (a), and (c) a patch of turbulence, case TP2 with a different initial energy spectrum with higher small-scale content. The evolution of the fluctuations is found to be strongly dependent on the initial energy spectrum, e.g., in case TP2, the kinetic energy is substantially smaller, and the late-wake vortices are less organized. The effect of the mean velocity field is negligible for mean kinetic energy (MKE) of the order 10% of the total kinetic energy and the evolution in this case is similar to a turbulent patch with the same initial energy spectrum. Increasing the MKE to 50% shows significant difference from the turbulent patch with the same initial energy spectrum during the initial stages of the evolution, but at later stages the evolution of turbulence statistics is similar. Both the turbulent patch and the momentumless wake show layering and formation of pancake eddies owing to buoyancy. Another objective of the paper is to compare the spatially evolving wake with the temporally evolving approximation when the initial near-wake condition of the temporal approximation is chosen to match the inflow of the spatially evolving model. The mean and turbulent flow statistics are found to agree well between the spatial and temporal computational models under these conditions.