Matthew B. de Stadler

Effect of the Prandtl number on a stratified turbulent wake

Direct numerical simulation is employed to study the effect of the Prandtl number, Pr=ν/α with ν the molecular viscosity and α the molecular diffusivity, on a turbulent wake in a stratified fluid. Simulations were conducted at a Reynolds number of 10 000, Re=UD/ν with U the velocity of the body and D the diameter of the body, for a range of Prandtl numbers: 0.2, 1, and 7. The simulations were run from x/D=6 to x/D=1200, a range that encompasses the near, intermediate, and far wake. Mean quantities such as wake dimensions and defect velocity were found to be weakly affected by Prandtl number, the same result was observed for vorticity as well. The Prandtl number has a strong effect on the density perturbation field and this results in a number of differences in quantities such as the total energy of the wake, wave flux, scalar and turbulent dissipation, mixing efficiency, spectral distribution of energy in the density and velocity fields, and the transfer of energy between kinetic and potential modes. The ...

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

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. In...

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

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.