Aspects of the propagation of an Internal Solitary Wave of depression over flat and gently varying bathymetry

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The propagation of an Internal Solitary Wave (ISW) of depression is explored through highly-accurate numerical simulations, over a flat surface and gently varying bathymetry. The interaction between the ISW and the bottom bed may produce sediment resuspension capable of influencing bed morphology, facilitate nutrient access for organisms living in the water column, and possibly impact the integrity of bottom-lodged structures. As the wave shoals over gently varying bathymetry, an instability may develop, inducing convective breaking and causing the formation of a trapped, or recirculating core. The turbulent flow inside the core dissipates kinetic energy, mixes the fluid, and transports suspended material material, in the water column, across large distances. To understand the impact of the propagating ISW over the bottom bed, the pore-pressure field is examined using high-accuracy numerical simulations. The velocity and density fields are obtained by solving the Dubreil-Jacotin-Long (DJL) Equation, for a two-layer, continuously stratified water column. The total wave-induced pressure across the surface of the bed is computed by vertically integrating for the hydrostatic and nonhydrostatic contributions. The bed is assumed to be a continuum composed of either sand or silt, with a small amount of trapped gas. Results indicate variations in pore-water pressure penetrating deeper into more conductive materials and remaining for a prolonged period after the wave has passed. In order to quantify the potential for failure, the vertical pore-pressure gradient is compared against the buoyant weight of the bed. The pressure gradient exceeds this weight for weakly conductive materials. Failure is further enhanced by a decrease in bed saturation, consistent with studies in surface-wave induced failure. In deeper water, the ISW-induced pressure is stronger, causing failure only for weakly conductive materials. The pressure associated with the free-surface displacement that accompanies ISWs is significant, when the water depth is less than 100m, but has little influence when it is greater than 100m, where the hydrostatic pressure due to the pycnocline displacement is much larger. Since the pore-pressure gradient reduces the specific weight of the bed, results show that particles are easier for the flow to suspend, suggesting that pressure contributes to the powerful resuspension events observed in the field. When an ISW propagates over gently varying bathymetry, a trapped, or recirculating, subsurface core may develop as a consequence of a preceding convective instability. Its formation is explored through fully nonlinear and non-hydrostatic two-dimensional simulations. The computational approach is based on a high resolution/accuracy deformed spectral multidomain penalty method (SMPM) flow solver, which incorporates observed background current and stratification profile \cite{lien2014}, along with recorded bathymetry, from the South China Sea. Given these field conditions, the SMPM flow solver is initialized using the solution of the fully-nonlinear Dubreil-Jacotin-Long (DJL) Equation. During shoaling, convective breaking precedes core formation, as the ISW-rear steepens and the trough decelerates; heavier fluid plunges forward and becomes trapped. This breaking mechanism is attributed to the stretching of the near-surface vorticity layer of the baroclinic background current. Since the sign of the vorticity is opposite to that of the propagating wave, only subsurface recirculating cores can be obtained. Once the core is established, the ISW propagates preserving its symmetric waveform. The onset of convective breaking is visualized, along with quantifying the sensitivity of the core properties to changes in the initial wave, near-surface background velocity, and maximum slope of the measured bathymetry. Various methods of defining the subsurface core boundary are explored and compared with field observations. The simulations capture the development of the recirculating subsurface core, but not the observed wave properties. The Richardson number and lateral vorticity are used to investigate the presence of shear instabilities of Kelvin-Helmholtz (KH) type, possibly preceding the convective instability. Results in indicate that these may occur as a consequence of the convective instability, but not as an individual event. A three-dimensional simulation is initialized prior to convective breaking and the ISW is then allowed to propagate until convective breaking occurs. As the wave shoals, three-dimensional breaking ensues, but no turbulent flow is simulated. Lateral convective instabilities develop due to the primary convective overturn. The evolution of the Kinetic Energy (KE) and Available Potential Energy (APE) suggests that KE is extracted from the background current and converted to APE through the buoyancy flux. Overall, the results constitute a baseline for future three-dimensional simulations aimed at exploring the turbulent flow inside the core.

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Trapped (Recirculating) Cores; Fluid Mechanics; Convective Instability; ISW-induced bottom pressure; Shoaling Internal Solitary Waves (ISW) of Depression; Shoaling ISW over gentle slopes


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Diamessis, Peter J.

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Jenkins, James Thomas
Desjardins, Olivier

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Civil and Environmental Engineering

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Ph. D., Civil and Environmental Engineering

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Doctor of Philosophy

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dissertation or thesis

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