Simulation of a propelled wake with moderate excess momentum in a stratified fluid

Abstract

Direct numerical simulation is used to simulate the turbulent wake behind an accelerating axisymmetric self-propelled body in a stratified fluid. Acceleration is modelled by adding a velocity profile corresponding to net thrust to a self-propelled velocity profile resulting in a wake with excess momentum. The effect of a small to moderate amount of excess momentum on the initially momentumless self-propelled wake is investigated to evaluate if the addition of excess momentum leads to a large qualitative change in wake dynamics. Both the amount and shape of excess momentum are varied. Increasing the amount of excess momentum and/or decreasing the radial extent of excess momentum was found to increase the defect velocity, mean kinetic energy, shear in the velocity gradient and the wake width. The increased shear in the mean profile resulted in increased production of turbulent kinetic energy leading to an increase in turbulent kinetic energy and its dissipation. Slightly larger vorticity structures were observed in the late wake with excess momentum although the differences between vorticity structures in the self-propelled and 40 % excess momentum cases was significantly smaller than suggested by previous experiments. Buoyancy was found to preserve the doubly inflected velocity profile in the vertical direction, and similarity for the mean velocity and turbulent kinetic energy was found to occur in both horizontal and vertical directions. While quantitative differences were observed between cases with and without excess momentum, qualitatively similar evolution was found to occur.