Internal hydraulic jumps in two-layer flows with upstream shear
Ogden, Kelly A.
Helfrich, Karl R.
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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.
Author Posting. © The Author(s), 2015. This is the author's version of the work. It is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 789 (2016): 64-92, doi:10.1017/jfm.2015.727.