Internal solitary waves (ISWs) are long waves which are ubiquitous throughout the stratified ocean. These waves maintain a uniquely near-steady wave form through their characteristic balance between strong nonlinear and non-hydrostatic effects. As energy cascades down the oceanic scale continuum into ISWs, instabilities develop within the waves which drive turbulent dissipation and mixing far from the wave generation site. Some of the largest ISWs ever observed in-situ are those occurring over the continental slope and shelf of the South China Sea (SCS). Observations in the SCS have revealed convectively unstable, large-amplitude shoaling ISWs with recirculating turbulent cores in their interior. Within the cores, massive O(100 m) density overturns develop supporting dissipation and mixing estimated to be O(1000) greater than in the open ocean. Through a close-knit integration of extensive observational data and high-accuracy/resolution simulations, this project has aimed to provide an improved understanding of the mechanisms of ISW convective instability and resulting turbulence.

Essential to the project's objectives has been the development of a state-of-the-art Fourier-Galerkin/Spectral-Element incompressible Navier-Stokes solver by our co-PI Diamessis. This is custom-built to simulate the development of turbulence within nonlinear internal waves propagating over long distances in variable depth waters. The process code design, implementation and benchmarking has adhered to the industry-quality software engineering standards yielding cutting edge computational technology. The code exhibits excellent parallel performance, scaling up to 6,000 cores on NSF XSEDE systems for 350 million grid points (ideal for the study of the multiscale physics of interest).

An extensive analysis of observations of hundreds of ISWs sampled over a period of 5-to-11 months on the upper continental slope of the SCS established, for a much larger dataset, the universality of the scenario originally posited: convective instability occurs within a shoaling ISW as it decelerates upon entry into shallower waters, with the wave-induced current overtaking the wave propagation speed. Moreover, the convectively breaking ISWs are proposed to operate in a marginally unstable state: their maximum current and propagation speeds remain equal and decrease at nearly the same rate, adjusting to the gradually sloping bottom.

Two-dimensional simulations of highly nonlinear ISWs over idealized bathymetry were first used to elucidate the mechanisms of recirculating core formation following convective instability during ISW shoaling over gentle slopes. Whether a recirculating trapped core is formed, in this case, below the sea surface (vs. at the surface) is largely determined by the sign of the vorticity of the near-surface background current. Subsequent two-dimensional simulations, over a 75km-long SCS bathymetric transect with realistic background stratification and current profiles, tracked the evolution of individual ISWs from 900m water to 350m depth.

The above mechanism of convective instability, due to ISW deceleration in shallower waters, was again confirmed. The size of the convective breaking region was found to be set by the amplitude (maximum isopycnal displacement) of the initial, deep-water, wave and magnitude of the near-surface background current vorticity. Slope steepness at this location only accelerates recirculating core formation. For the same bathymetry and background current/stratifications, unprecedented, massively parallel, three-dimensional turbulence-resolving simulations (with resolutions of 1m or less in all three directions) were conducted for three cases of deep-water waves with amplitudes of 136m, 143m and 150m. In all runs, the isopycnal plunging from the rear of the wave during the onset of convective breaking evolves into a gravity-current-like feature propagating across the wave interior. The spatial extent and intensity of the actively turbulent region within the wave is a function of wave amplitude. The rear half of the wave interior is mixed by the turbulence, thereby weakening the stratification at the wave trough allows where shear instabilities then form, a phenomenon not reproduced by two-dimensional simulations. Billow vortices propagate out of the rear of the wave, supporting overturns as high as 25m . For the 150m amplitude wave, the billow vortices persistently extract energy from the wave efficiently enough to drive a distinct turbulent wake in the ISW rear. Turbulent velocities in the heart of the recirculating core and the shear-instability-driven billows are as high as 10% of the wave-induced currents suggesting an extremely energetic flow field.

Despite the persistent intense turbulence in the ISW core and wake, the wave form remains remarkably symmetric throughout the entire wave evolution. The modeling component of this collaborative program has provided unprecedented spatiotemporal detail on the mechanisms operative during the convective breaking of a large-amplitude ISW and the shear instability subsequently generated. From an observational standpoint, the established universality of convective breaking within the SCS suggests that such ISWs are likely to occur in other regions rich in high-amplitude waves. Moreover, the proposed evolution of these waves in a marginally unstable manner further indicates that they contribute to turbulent mixing over long distances along the wave propagation path. Numerous questions have emerged regarding the design of future simulations and field deployments.

Last Modified: 10/28/2022
Modified by: Ren-Chieh Lien