Internal solitary wave-induced flow over a corrugated bed

Abstract

A combined numerical and experimental study of the propagation of an internal solitary wave (ISW) over a corrugated bed is presented, in which the amplitude and the wavelength of the corrugated bed, together with the wave amplitude and wave speed of the ISW, have been varied parametrically. Both ISWs of elevation and depression have been considered. The wave-induced currents over the corrugated bed cause flow separation at the apex of the corrugations and a sequence of lee vortices forms as a result. These vortices develop fully after the main wave has passed over the topographic feature, resulting in deformation of the overlying pycnocline and, in some instances, significant vertical mixing. It is found that the intensity of the vortex formation is dependent on both the amplitude and wavelength of the bottom topography. In the case of an ISW of depression, the generation of vertically (upward)-propagating vortices is seen to result in entrainment of fluid from a bottom boundary jet (Carr

Numerical simulations of shoaling internal solitary waves of elevation

“…Unlike in the experiments and simulations performed by Carr et al (2010) where vortices are subsequently formed from these corrugations, in our simulation the flow inside these 'valleys' is not energetic enough to self advect away from the boundary layer. In fact, as shown in figure 3.16, the magnitudes of the negative vorticity, horizontal velocity and bottom shear stress induced by the downstream-directed flow in the trough of the corrugations are only a fraction of those found in the main flow above the boundary layer.…”

“…However, because the amplitudes of these corrugations are very small, the flow is not energetic enough to self advect away from the boundary layer. As suggested in Carr et al (2010), the energy carried by the flow inside these corrugations is determined by the size and shape of these corrugations, as well as the stratification of the fluid. To further understand the influence a rough bottom topography on the behaviour of the shoaling wave, experiments with various types of the bottom corrugations will need to be carried out.…”

“…Because the trapped core of ISWs of elevation interacts directly with the BBL during the shoaling process, any perturbation to the bottom topography will necessarily alter the nature of the flow. A combined experimental and numerical study of ISWs propagating over a corrugated bottom boundary has been reported in Carr et al (2010). In the case of waves of elevation, it is found that two different mechanisms are responsible for the generation of turbulent mixing in the water column: the boundary layer separation at the crest of each individual corrugation caused by the ISW-induced current, from which lee vortices are subsequently formed, and the shear instability in the upstream portion of the wave, which occurs when the bottom corrugations reach into (or very close to) the pycnocline at rest.…”

“…For example, the lee vortices which are absent in the present simulation may appear in field scale simulations. In addition, Carr et al (2010) also suggest that variation of wavelength and amplitude of the bottom corrugations will affect the resulting turbulent mixing, because these properties are directly related to the amount of energy carried by the flow inside these corrugations. Therefore, to further understand this topic, the next step is to experiment with field scale flows and various sizes and shapes of bottom corrugations.…”

Topographically generated internal waves and boundary layer instabilities

“…This has been suggested by multiple authors in field, experimental, and numerical work. 1,7,12,17 Recent numerical work has confirmed that sediment resuspension occurs in a coupled hydrodynamic-sediment model. 6 More broadly, a wide variety of field studies have pointed to a link between increased near-bed sediment concentrations and shoaling internal waves on a slope.…”