Internal solitary wave shoaling
Internal solitary waves (ISWs) are finite amplitude waves of permanent form that travel along density interfaces in stably stratified fluids. They owe their existence to an exact balance between non-linear wave steepening effects and linear wave dispersion. They are common in all stratified flows especially coastal seas, straits, fjords and the atmospheric boundary layer. Whilst ISWs can travel considerable distance over a flat bottom without change of form, under certain conditions, such as when shoaling, their form can change considerably. As they do so, dissipation produced by the motion of breaking waves, both in the benthic boundary layer and the pycnocline, is identified as a key process in the global cascade of energy from global-scale mechanical forcing to dissipation. In this presentation a combined experimental and numerical study will illustrate the effect of stratification form on the shoaling characteristics of ISWs propagating over a smooth, linear topographic slope. It is found that the form of stratification affects the breaking type associated with the shoaling wave. In a thin tanh stratification (homogeneous upper and lower layers separated by a thin pycnocline), good agreement is seen with past studies. Waves over the shallowest slopes undergo fission. Over steeper slopes, the breaking type changes from surging, through collapsing to plunging with increasing wave steepness Aw/Lw for a given topographic slope, where Aw and Lw are incident wave amplitude and wavelength, respectively. In a surface stratification regime (linearly stratified layer overlaying a homogeneous lower layer), the breaking classification differs from the thin tanh stratification. Plunging dynamics are inhibited by the density gradient throughout the upper layer, instead collapsing-type breakers form for the equivalent location in parameter space in the thin tanh stratification. In the broad tanh profile regime (continuous density gradient throughout the water column), plunging dynamics are likewise inhibited and the near-bottom density gradient prevents the collapsing dynamics as well. Instead, all waves either fission or form surging breakers. As wave steepness in the broad tanh stratification increases, the bolus formed by surging exhibits evidence of Kelvin–Helmholtz instabilities on its upper boundary. In both two- and three-dimensional simulations, billow size grows with increasing wave steepness, dynamics not previously observed. If time, shoaling mode-2 ISWs will be also considered. Features of wave shoaling include (i) formation of an oscillatory tail, (ii) degeneration of the wave form, (iii) wave run up, (iv) boundary layer separation, (v) vortex formation and re-suspension at the bed and (vi) a reflected wave signal. In shallow slope cases, the wave form is destroyed by the shoaling process; the leading mode-2 ISW degenerates into a train of mode-1 waves of elevation and little boundary layer activity is seen. For steeper slopes, boundary layer separation, vortex formation and re-suspension at the bed are observed. The boundary layer dynamics are shown (numerically) to be dependent on the Reynolds number of the flow.