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Woods Hole Oceanographic Institution

Karl R. Helfrich

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Publications
»Internal hydraulic jumps in two-layer flows with upstream shear
»Isolating the hydrodynamic triggers of the diver response in the larval eastern oyster (Crassostrea virginica)
»Whales and waves: humpback whale foraging response and the shoaling of internal waves at Stellwagen Bank
»The formation and fate of internal waves in the South China Sea
»Laboratory experiments and simulations for solitary internal waves with trapped cores
»Internal bores in continuous stratifications
»Combined effect of rotation and topography on shoaling oceanic internal solitary waves
»Large-scale, realistic laboratory modeling of the M2 internal tide generation at the Luzon Strait
»Upward swimming of competent oyster larvae
»Experimental study of the effect of rotation on nonlinear internal waves
»Rapid gravitational collapse of a horizontal shear layer
»Swimming behavior and velocities of barnacle cyprides in a downwelling flume
»The effect of rotation on internal solitary waves
»A general description of a gravity current front propagating in a two-layer stratified fluid
»The reduced Ostrovsky equation: integrability and breaking
»Strongly nonlinear, simple internal waves in continuously-stratified, shallow fluids
»A model of internal solitary waves with trapped cores
»Synthetic aperature radar observations of resonantly generated internal solitary waves at Race Point Channel (Cape Cod)
»The skirted island: the effect of topography on the flow around planetary scale islands
»Continuously stratified nonlinear low-mode internal tides.
»Gravity currents and internal waves in a continuously stratified fluid
»Long-time solutions of the Ostrovsky equation
»Nonlinear disintegration of the internal tide
»On the stability of ocean overflows
»A transverse hydraulic jump in a model of the Faroe Bank Channel outflow
»Decay and return of rotating internal solitary waves
»Mixing at the head of a canyon: A laboratory laboratory investigation of fluid exchanges in a rotating, stratified basin
»Nonlinear adjustment of a localized layer of buoyant fluid against a vertical wall
»Long Nonlinear Internal Waves
»Generalized conditions for hydraulic criticality of oceanic overflows
»Gravity currents from a dam-break in a rotating channel
»A laboratory study of localized boundary mixing in a rotating stratified fluid
»Mixing and entrainment in hydraulically-driven, stratified sill flows


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Ogden, K. A. and K.R. Helfrich, Internal hydraulic jumps in two-layer flows with upstream shear, J. Fluid Mech, in press

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.

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