Simulation of a self-propelled wake with moderate excess momentum in a homogeneous fluid

Abstract

Direct numerical simulation was used to simulate a self-propelled wake with excess momentum in a homogeneous fluid. Simulations were performed with varying distributions and amounts of excess momentum. Both the shape and amount of excess momentum were found to result in larger initial values of the defect velocity, mean kinetic energy, and velocity gradient. Increasing the amount of excess momentum resulted in larger dierences from a self-propelled wake with zero net momentum for the mean kinetic energy and defect velocity although dierences among cases for fluctuation and turbulent statistics were smaller consistent with qualitatively similar evolution. At early time, a smaller radial extent of the excess momentum results in a larger dierences from a self-propelled wake with zero net momentum than a case with a larger radial extent and the same amount of excess momentum. However, at intermediate to late time, statistics are comparable between the two cases. The initially doubly-inflected mean velocity profile was lost in all cases with the self-propelled and small excess momentum (5%) cases exhibiting no discernible structure beyond early time and the intermediate momentum (20,40%) cases transitioning to a bell shaped profile typical of a momentum wake. A brief discussion is included comparing the dierences between wakes with excess momentum in a stratified and homogeneous fluid. Overall, while quantitative dierences were observed with larger amounts of excess momentum and/or momentum applied over a smaller radial extent, there was little qualitative dierence over the range of values considered in this study.