Numerical Investigation of Solitary Internal Wave-Induced Global Instability in Shallow Water Benthic Boundary Layers

Abstract

The time-dependent boundary layer induced by a weakly nonlinear solitary internal wave in shallow water is examined through direct numerical simulation. Waves of depression and elevation are both considered. The mean density field corresponds to that typical of the coastal ocean and lakes where the lower fraction of the water column is subject to the stabilizing effect of a diffuse stratification. Sufficient resolution of the “inviscid” dynamics of the boundary layer is ensured through use of a Legendre spectral multidomain discretization scheme in the vertical direction. At higher Reynolds numbers, where the simulations become underresolved, because of restrictions in available computational resources, spectral accuracy and numerical stability at the scales of physical interest are preserved through use of a penalty scheme in the vertical and explicit spectral filtering. Thus, a highly accurate description of the qualitative dynamics of the wave-induced global instability is possible and finescale physical mechanisms critical to the appearance of this instability are not smeared out by the high artificial dissipation inherent in lower-order finite-difference schemes. Results indicate that, for a wave amplitude exceeding a critical value, the global instability occurs in regions near the bottom boundary where the wave induces an adverse pressure gradient. The structure of the associated separation bubble is modified through the establishment of coherent and synchronous dynamics, characterized by elevated levels of bottom shear stress and a periodic shedding of coherent vortex structures. Although details of the vortex shedding depend on the particular wave forcing involved, these vortical structures always ascend high into the water column. All findings suggest that this global instability is a potent mechanism for benthic turbulence, mixing, and possible sediment resuspension in shallow waters, presumably even more intense than the nominal turbulent boundary layer.

Numerical simulations of shoaling internal solitary waves of elevation

“…Two-dimensional numerical simulations suggest that shear instability (Helfrich and White, 2010;Carr et al, 2012) and boundary layer instability (Diamessis and Redekopp, 2005;Stastna and Lamb, 2008) can occur in both waves of elevation and depression. The shear instability occurs along the edge of the cores and takes the form of Kelvin-Helmholtz billows, leading to fluid exchange between the cores and the ambient flow.…”

Benthic Turbulence and Mixing Induced by Nonlinear Internal Waves

“…The two NLIWs recorded by the SeaBASS on JD 242.21 and 242.23 have amplitudes 0.07 and 0.15, respectively. Both of these amplitudes exceed the critical value for global instability extrapolated to the field Reynolds number of 10 7 (based on the findings of Diamessis and Redekopp (2006a) and adjusted according to the laboratory observations of Carr et al (2007) for fully non-linear internal waves). Thus, the distinct qualitative similarities between DNS and CMO 96 observations and the low critical wave amplitude value (approximately 10%) at oceanically relevant Reynolds numbers suggest that NLIWs capable of producing distinct benthic eruptions are relatively low-amplitude waves and occur frequently on the continental shelf.…”

Boundary layer flow beneath an internal solitary wave of elevation

“…They concluded that an upstream source of vorticity was vital for vortex shedding to occur and the presence of a separation bubble was not necessarily required. Diamessis and Redekopp 16 recently extended the earlier work of Bogucki and Redekopp 13 and Wang and Redekopp 14 to ISWs of depression and ISWs of elevation propagating in an unsheared flow. They found separation of the boundary layer in the adverse pressure gradient region and the formation of vortices in both cases.…”

“…The primary interest in this paper lies in the behavior of ISWs of elevation. In this regard, theoretical investigations [12][13][14][15][16] of the interaction between an ISW of elevation and a flat bottom boundary have shown that the boundary layer can separate in the adverse pressure gradient region in the front part of the wave and vortices may be formed beneath the center of the ISW. Bogucki and Redekopp 13 and Wang and Redekopp 14 employed as forcing a two-dimensional direct numerical simulation with a weakly nonlinear ISW of elevation, propagating against a linearly sheared flow.…”