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Numerical investigation of momentumless wakes in stratified fluids

  • Author(s): Brucker, Kyle Ashley
  • et al.
Abstract

The dissertation focuses on a comparison between momentumless (self-propelled) and net-momentum (towed) wakes with an emphasis on the elucidation of buoyancy effects. It is difficult to realize truly momentumless wakes in the laboratory and DNS offer a viable, accurate alternative because the initial value of net momentum can be controlled and the evolution of the net momentum can be closely monitored. DNS of axisymmetric wakes with and without net momentum are performed at Re=50,000 on a grid with approximately 2 billion grid points. The development of the wake is characterized by the evolution of maxima, area integrals and spatial distributions of mean and turbulence statistics. The mean velocity in the self- propelled, momentumless wake decays more rapidly than the towed case due to higher shear and consequently a faster rate of energy transfer to turbulence. Buoyancy allows a wake to survive longer in a stratified fluid by reducing the correlation responsible for the mean-to- turbulence energy transfer in the vertical direction. This buoyancy effect is especially important in the self- propelled case because it allows regions of positive and negative momentum to become decoupled in the vertical direction and decay with different rates. The vertical wake thickness is found to be larger in self-propelled wakes. The role of internal waves in the energetics is determined and it is found that they are responsible for sustaining turbulence at the wake periphery long after the shear production has subsided. The non-equilibrium region of the Re=50,000 wake is found to exhibit a time span when, although the turbulence is strongly stratified as indicated by small Froude number, the turbulent dissipation rate exhibits inertial scaling. The multiply inflected mean velocity profile, inherent to the self- propelled wake, results in four bands of vorticity, compared to the two bands observed in the towed case. Vortex pairs of opposite sign form vortex dipoles which interact with other dipoles to cause a more disordered appearance of the late wake vorticity when compared to the towed case.

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