Ogden Kelly A.

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Ogden
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Kelly A.
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  • Preprint
    Internal hydraulic jumps in two-layer flows with upstream shear
    ( 2015-12-04) Ogden, Kelly A. ; Helfrich, Karl R.
    Internal hydraulic jumps in ows with upstream shear are investigated using two-layer shock-joining theories and numerical solutions of the Navier-Stokes equations. The role of upstream shear has not previously been thoroughly investigated, although it is important in many oceanographic situations, including exchange ows. The full solution spaces of several two-layer theories, distinguished by how dissipation is distributed between the layers, with upstream shear are found, and the physically allowable solution space is identi ed. These two-layer theories are then evaluated using more realistic numerical simulations that have continuous density and velocity pro les and permit turbulence and mixing. Two-dimensional numerical simulations show that none of the two-layer theories reliably predicts the relation between jump height and speed over the full range of allowable solutions. The numerical simulations also show that di erent qualitative types of jumps can occur, including undular bores, energy-conserving conjugate state transitions, smooth front jumps with trailing turbulence, and overturning turbulent jumps. Simulation results are used to investigate mixing, which increases with jump height and upstream shear. A few three-dimensional simulations results were undertaken and are in quantitative agreement with the two-dimensional simulations.
  • Thesis
    Internal hydraulic jumps with upstream shear
    (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 2017-02) Ogden, Kelly A.
    Internal hydraulic jumps in flows with upstream shear are investigated numerically and theoretically. The role of upstream shear has not previously been thoroughly investigated, although it is important in many oceanographic flows such as exchange flows and stratified flow over topography. Several two-layer shock joining theories, characterized by their distribution of dissipation in the jump, are considered and extended to include upstream shear, entrainment, and topography. Theoretical results are also compared to 2D and some 3D numerical simulations of the full Navier-Stokes equations, which allow continuous velocity and density distributions. The solution space of idealized jumps with small upstream shear is identified using twolayer theories, which shows that upstream shear allows larger jumps to form and allows jumps for a larger range of parameters. Numerical simulations reveal several jump structures that can occur in these flows, including an undular bore, a fully turbulent jump, and a smooth front turbulent jump. At low shear, the 2D mixing efficiency is constant across simulations. As shear increases, the basic two-layer theories no longer provide solutions. Numerical simulations show that entrainment becomes significant as the shear increases, and adding entrainment and shape parameters to describe the continuous velocity profiles is required to accurately describe the simulations using two-layered theory. The entrainment depends on the upstream shear and can be predicted with a modified theory. However, use of the theory is limited due to its sensitivity to the value of the shape parameters. The 2D mixing efficiency also decreases significantly as shear increases. Finally, more realistic 2D and some 3D simulations including topography bridge the gap between the highly idealized simulations and the very realistic work of others. Simulations with topography show additional jump types, including a higher mode jump with a wedge of homogeneous, stagnant fluid similar to a structure seen in Knight Inlet. In all cases, numerical simulations are used to identify trends in the mixing and jumps structures that can occur in internal hydraulic jumps.