The dynamics of breaking internal solitary waves on slopes

Abstract

AbstractUsing direct numerical simulations (DNS), we investigate the structure and energetics of breaking internal waves on slopes. We employ a Navier–Stokes code in an idealized three-dimensional domain where an internal solitary wave of depression impinges upon a sloping bottom. Seven cases with varying initial wave amplitude and bathymetric slope, but constant wave Reynolds number $\mathit{Re}_{w}$ are considered. Volume-integrated values of dissipation and irreversible mixing are related to the density and velocity structure of the wave throughout the breaking process. The majority of dissipation (63 %) occurs along the no-slip bottom boundary. Most of the remaining dissipation (35 %) and nearly all irreversible mixing occurs in the interior after breaking, when density overturns are present at the interface. Breaking introduces three-dimensionality to the flow field that is driven by the lateral breakdown of density overturns and the lobe–cleft instability typical of gravity currents. The resulting longitudinal rolls (streamwise vorticity) increase dissipation by roughly 8 % and decrease irreversible mixing by roughly 20 % when compared with a similar two-dimensional simulation. The bulk mixing efficiency is shown to increase for larger and smaller values of the internal Iribarren number ${\it\xi}$, with a minimum for intermediate values of ${\it\xi}$ and a peak near ${\it\xi}=0.8$ for plunging breakers. This trend is explained by the degree of two-dimensionality in the flow, and agrees with previous results in the literature after accounting for Reynolds number effects. Local turbulence quantities are also calculated at ‘virtual moorings’, and a location upslope of the breakpoint but downslope of the intersection of the pycnocline and the bottom is shown to provide a signal that is most representative of the volume-integrated dissipation and mixing results.