Publication Date:
2022-05-25
Description:
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2017
Description:
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.
Description:
This work was supported by National Science Foundation grant OCE-1029672, the H. B.
Bigelow Chair of the Woods Hole Oceanographic Institution, and the Natural Sciences and
Engineering Research Council of Canada.
Repository Name:
Woods Hole Open Access Server
Type:
Thesis
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