Ogden, K. A. and K.R. Helfrich, Internal hydraulic jumps in twolayer flows with upstream shear, J. Fluid Mech, in press
Internal hydraulic jumps in flows with upstream shear are investigated using twolayer shockjoining theories and numerical solutions of the NavierStokes 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 twolayer theories, distinguished by how dissipation is distributed between the layers, with upstream shear are found, and the physically allowable solution space is identified. These twolayer theories are then evaluated using more realistic numerical simulations that have continuous density and velocity profiles and permit turbulence and mixing. Twodimensional numerical simulations show that none of the twolayer 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, energyconserving 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 threedimensional simulations results were undertaken and are in quantitative agreement with the twodimensional simulations.
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