Boundary layer flow beneath an internal solitary wave of elevation

Abstract

The wave-induced flow over a fixed bottom boundary beneath an internal solitary wave of elevation propagating in an unsheared, two-layer, stably stratified fluid is investigated experimentally. Measurements of the velocity field close to the bottom boundary are presented to illustrate that in the lower layer the fluid velocity near the bottom reverses direction as the wave decelerates while higher in the water column the fluid velocity is in the same direction as the wave propagation. The observation is similar in nature to that for wave-induced flow beneath a surface solitary wave. Contrary to theoretical predictions for internal solitary waves, no evidence for either boundary layer separation or vortex formation is found beneath the front half of the wave in the adverse pressure gradient region of the flow.

Numerical simulation of internal solitary wave—induced reverse flow and associated vortices in a shallow, two-layer fluid benthic boundary layer

“…The initial flow reversal has been attributed to boundary layer (BL) separation in the adverse pressure gradient region aft of the wave. However, Carr and Davies (2010) have recently observed a similar nearbed flow reversal under the rear part of an ISW of elevation. In this case, the pressure gradient is favourable aft of the wave and, hence, the flow reversal there cannot be due to the same BL separation mechanism proposed above for ISWs of depression.…”

Internal solitary wave-induced flow over a corrugated bed

“…Table 2 gives a comparison, in the depression experiments, of the ISW and corrugated bed wavelengths and amplitudes, respectively. The Reynolds number of the wave as defined in Carr et al (2008) and Carr and Davies (2010) varied from 2.5 × 10 4 to 2.6 × 10 4 in the depression experiments and from 5.0 × 10 4 to 7.6 × 10 4 in the elevation experiments.…”

“…Near bottom grid spacing up to 1 mm yielded qualitatively unchanged results. The Reynolds number defined following Carr et al (2008) and Carr and Davies (2010) was varied between 1.25 × 10 4 < Re < 5 × 10 4 , with the larger value used in all numerical figures. The dynamics remained qualitatively unchanged for this range of wave Reynolds number.…”

“…For large-amplitude ISWs propagating over a smooth flat bottom, laboratory experiments and numerical simulations have demonstrated that ISWinduced currents can lead to hydrodynamic instabilities in the bottom boundary layer (BBL) (Stastna and Lamb 2002;Diamessis and Redekopp 2006;Carr et al 2008;Stastna and Lamb 2008;Carr and Davies 2010). In the ocean, non-uniform bottom topography is expected to alter the ISW-induced BBL flow.…”

Simulation of the Navier–Stokes equations in three dimensions with a spectral collocation method

“…In viscous simulations, these currents produce boundary layers at no-slip boundaries (generally the bottom of the domain), creating strong shear. For particularly large internal waves, this shear has the potential to become unstable [Carr and Davies, 2010;Diamessis and Redekopp, 2006]; this section focuses on the less-intense case of smaller-scale waves left to propagate for long times 5 , in or- Figure 4.7: Three-dimensional view of the simulation of wave 4a, showing the ρ = 1 isosurface shaded by the spanwise velocity in the tail of the wave. The threedimensional evolution of the billows is first characterized by production of spanwise velocity, which then affects the three-dimensional shape of density isosurfaces.…”