Helical Coherent Structures in the Wake of Solitary Internal Waves Breaking on the Continental Slope

Mixing caused by the solitary internal waves or solitons in stratified coastal waters is a primary cause of sediment resuspension and transport. Theoretical, experimental, and modeling studies of solitons have focused on nonlinear wave dynamics to explain their main features. However, the 3D cascade of energy from breaking internal wave solitons to turbulence and mixing in the wave induced wake has received less attention. Observations on the California shelf with a spatially distributed fiber optic sensing system revealed coherent structures in the wake of solitary internal waves breaking on the continental slope1,2. Here, we reproduced this phenomenon with a computational fluid dynamics model. The model demonstrated that the coherent structures in the wake of the breaking solitary internal wave are counterrotating helices. The concept of helicity3 as a topological invariant and a measure of the lack of mirror symmetry of the flow can explain the helical nature of these coherent structures4. Both observational and modeling results are consistent with this theoretical conjecture. These coherent structures have a substantial effect on the sediment transport in the bottom boundary layer, formation of nepheloid layers5, and nutrient fluxes.

Laboratory experiments and simulations for solitary internal waves with trapped cores

We perform simultaneous coplanar measurements of velocity and density in solitary internal waves with trapped cores, as well as viscous numerical simulations. Our set-up 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 instability, and use our velocity measurements to perform quantitative calculations supporting this hypothesis. These surface-tension effects appear to be difficult 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 agreement. 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 that 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.

Mass and momentum transfer by solitary internal waves in a shelf zone

The evolution of large amplitude internal waves propagating towards the shore and more specifically the run up phase over the "swash" zone is considered. The mathematical model describing the generation, interaction, and decaying of solitary internal waves of the second mode in the interlayer is proposed. The exact solution specifying the shape of solitary waves symmetric with respect to the unperturbed interface is constructed. It is shown that, taking into account the friction on interfaces in the mathematical model, it is possible to describe adequately the change in the phase and amplitude characteristics of two solitary waves moving towards each other before and after their interaction. It is demonstrated that propagation of large amplitude solitary internal waves of depression over a shelf could be simulated in laboratory experiments by internal symmetric solitary waves of the second mode.