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.

Influence of Propulsion Type on the Stratified Near Wake of an Axisymmetric Self-Propelled Body

“…Background turbulence increases the turbulent kinetic energy and energy transfer in the wake, which in turn lowers the mean velocity and increases horizontal spreading [19]. Excess momentum leads to changes in increased turbulent kinetic energy and qualitative changes in the wake dynamics, particularly in downstream vortical structures [20]. High levels of stratification in the wake create a non-equilibrium region in which the mean velocity decay is reduced [21,22].…”

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

“…The initial mean velocity profile used for the self-propelled wake cases SP50 and SP10 is identical to the canonical momentumless profile with positive and negative velocity lobes used in the previous work. 14,26 The defect velocity, U 0 for case SP50 is 0.3 whereas for case SP10, U 0 = 0.11, implying that SP50 has ∼50% mean kinetic energy of the total in comparison to ∼10% in SP10. As in our previous work, the initial velocity fluctuations are allowed to evolve during an adjustment period while the mean velocity profile is held fixed until the maximum value of u 1 u r /K −0.25, signifying that the cross-correlation has increased to a level typical of turbulent shear flow.…”

“…A fractional step method is used for integrating the Navier-Stokes equation as is briefly described by Brucker and Sarkar 14 and de Stadler and Sarkar. 26 Brucker and Sarkar 14 and de Stadler and Sarkar 26 used Red-black Gauss-Seidel method as a smoother for the multigrid method for solving the Poisson equation for pressure whereas in this study we use the same smoother with successive over relaxation (SOR) 27 to accelerate the convergence of the pressure Poisson equation on stretched grids in all three directions.…”

“…This result was in contrast to the result of Tennekes and Lumley, 22 derived on the basis of a selfsimilarity analysis that assumes constant eddy viscosity, that addition of even a small amount of excess momentum to the momentumless wake leads to a disproportionate change towards the longer life time of a towed wake. It is worth noting that the DNS 26 showed that an eddy viscosity cannot parametrize vertical mixing in the stratified wake where the vertical transport of momentum is oscillatory in space and time. Also of interest is the role of mean flow instabilities in the evolution of the coherent structures in the Q2D regime.…”

ALE–VMS formulation for stratified turbulent incompressible flows with applications

“…3 and 4), which are more challenging due to high computational costs associated with the need to use long computational domains and resolve small-scale turbulent fluctuations. 5 Stably-stratified atmospheric boundary layers (ABLs) present another set of challenges for modeling and simulation (see, e.g. Ref.…”