LuzzattoFegiz, P. and K. R. Helfrich , Laboratory experiments and simulations for solitary internal waves with trapped cores , J. Fluid Mech. submitted , 2014
We perform simultaneous, coplanar 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 noslip lid. In the freesurface case, all trappedcore 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 surfacetension 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 largeramplitude 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 threedimensional 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 quasisteady, 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 DubreilJacotinLong theory for waves with a uniformdensity, 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 TaylorGoldstein equation, we show that our results are consistent with empirical stability criteria in the literature.
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