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Internal hydraulic jumps in two-layer flows with upstream shear

Published online by Cambridge University Press:  15 January 2016

K. A. Ogden  and
Karl R. Helfrich
K. A. Ogden
Affiliation:
MIT/WHOI Joint Program in Oceanography, Cambridge, MA 02139, USA
Karl R. Helfrich*
Affiliation:
Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA 02536, USA
*
†Email address for correspondence: [email protected]
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Abstract

Internal hydraulic jumps in flows 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 flows. 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 identified. These two-layer theories are then evaluated using more realistic numerical simulations that have continuous density and velocity profiles 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 different 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.

JFM classification

Geophysical and Geological Flows: Hydraulic control Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 789 , 25 February 2016 , pp. 64 - 92
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Copyright
© 2016 Cambridge University Press 

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