The development of turbulence in convectively breaking internal solitary waves of depression shoaling over gentle slopes in the South China Sea*

We report on results from three-dimensional turbulence-resolving simulations of shoaling internal solitary waves (ISWs) over a gentle bathymetric slope and background stratification/current profiles directly sampled in the South China Sea. Under the realistic constraint of normal-to-isobath wave propagation, the massively parallel simulations leverage a custom-designed hybrid high-order spectral-element/Fourier-Galkerin flow solver (Diamantopoulos et al. 2022). Three values of initial ISW amplitude (max. isopycnal displacement) of 136m, 143m and 150m are considered. The O(1km)-long waves propagate from 900m to 350m depth waters over a distance of 75km. As soon as the ISW arrives at the steepest slope of the propagation track, a distinct convective instability develops with the outer waveform of the ISW remaining, nevertheless, distinctly symmetric. The isopycnal plunging from the rear of the wave during the onset of this instability effectively drives a turbulent gravity-current-like feature which propagates through the ISW interior. The rear half of the wave core is mixed giving rise to values of the Richardson number at the wave trough which are sufficiently low to trigger a shear-instability. The distinct Kelvin-Helmholtz billows which emerge, in the form of  15-20m overturns, are advected through the pycnocline out of the rear of the wave. In the case of the 150m-amplitude wave, the shear instability produces dramatically high levels of turbulent kinetic energy and gives rise to a visible wake of patchy turbulence and, apparently dispersive, lower-amplitude waves behind the ISW. The presentation concludes with the examination of the correlation of the along-propagation-track turbulent kinetic energy intensity with wave-scale properties and a discussion of the potential for marginal instability in the simulated ISWs.