Luzzatto-Fegiz, P. and K. R. Helfrich , 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. |