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.
