Kelly Ogden (MIT/WHOI)
"Internal Hydraulic Jumps with Upstream Shear
Internal hydraulic jumps in flows with upstream shear are investigated using two-layer shock-joining theories and numerical solutions of the Navier-Stokes equations. This phenomena is relevant in many oceanographic situations in which flows over topography or exchange flows result in upstream shear. The full solution spaces of internal hydraulic jumps with upstream shear are found using two-layer theories, which vary by how dissipation is distributed between the layers. The physically allowable solution space is identified as a subset of these solutions. The two-layer theories are compared to more realistic numerical simulations, which allow continuous density and velocity profiles and permit turbulence and mixing. The 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 jump types can occur, including undular bores, energy-conserving conjugate state transitions, smooth front jumps with trailing turbulence, and overturning turbulent jumps.
More realistic flows include complications such as bottom topography, time-dependent flow, and more detailed density stratifications. Numerical simulations are used to show that bottom topography allows additional jump types, including a higher mode jump with a wedge of homogeneous, stagnant fluid similar to a structure seen in Knight Inlet. These simulations are used to identify trends in the mixing and jumps structures that can occur in internal hydraulic jumps."