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Woods Hole Oceanographic Institution

Karl R. Helfrich

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Publications
»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
»Experimental study of the effect of rotation on nonlinear internal waves
»Upward swimming of competent oyster larvae
»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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Luzzatto-Fegiz, P. and K. R. Helfrich

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Laboratory experiments and simulations for solitary internal waves with trapped cores

, J. Fluid Mech. submitted , 2014

We perform simultaneous, co-planar measurements of velocity and density in solitary internal waves with trapped cores. Our setup comprises a thin stratified layer (approximately 15% of the overall fluid depth) overlaying a deep, homogeneous layer. We consider waves propagating near a free surface, as well as near a rigid no-slip lid. In the free-surface case, all trapped-core waves exhibit a strong shear instability. We propose that Marangoni effects are responsible for this effect, and use our velocity measurements to perform quan- titative calculations supporting this hypothesis. These surface-tension effects appear to be dicult to avoid at the experimental scale. By contrast, our experiments with a no- slip lid yield robust waves with large cores. In order to consider larger-amplitude waves, we complement our experiments with viscous numerical simulations, employing a longer, virtual tank. Where overlap exists, our experiments and simulations are in good agree- ment. In order to provide a robust definition of the trapped core, we propose bounding it as a lagrangian coherent structure (instead of using a closed streamline, as has been done traditionally). This construction is less sensitive to small errors in the velocity field, and to small three-dimensional effects. In order to retain only flows near equilibrium, we introduce a steadiness criterion, based on the rate of change of the density in the core. We use this criterion to successfully select within our experiments and simulations a family of quasi-steady, robust flows, which exhibit good collapse in their properties. The core circulation is small (at most, around 10% of the baroclinic wave circulation). The core density is essentially uniform; the standard deviation of the density, in the core region, is less than 4% of the full density range. We also calculate the circulation, kinetic energy, and available potential energy of these waves. We find that these results are consistent with predictions from Dubreil-Jacotin-Long theory for waves with a uniform-density, irrotational core, except for an offset, which we suggest is associated with viscous effects. Finally, by computing Richardson number fields, and performing a temporal stability analysis based on the Taylor-Goldstein equation, we show that our results are consistent with empirical stability criteria in the literature.


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