Shoaling mode-2 internal solitary-like waves

Abstract

The propagation of a train of mode-2 internal solitary-like waves (ISWs) over a uniformly sloping, solid topographic boundary, has been studied by means of a combined laboratory and numerical investigation. The waves are generated by a lock-release method. Features of their 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. Slope steepness, $s$, is defined to be the height of the slope divided by the slope base length. In shallow slope cases ($s\leqslant 0.07$), 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 ($s\geqslant 0.13$), boundary layer separation, vortex formation and re-suspension at the bed are observed. The boundary layer dynamics is shown (numerically) to be dependent on the Reynolds number of the flow. A reflected mode-2 wave signal and wave run up are seen for slopes of steepness $s\geqslant 0.20$. The wave run up distance is shown to be proportional to the length scale $ac^{2}/g^{\prime }h_{2}\sin \unicode[STIX]{x1D703}$ where $a,c,g^{\prime },h_{2}$ and $\unicode[STIX]{x1D703}$ are wave amplitude, wave speed, reduced gravity, pycnocline thickness and slope angle respectively.

Horizontal transport under wind-induced resonance in stratified waterbodies

“…6(i)]. A similar shoaling process for second-mode solitary waves has been recently reported in laboratory and numerical experiments by Carr et al [31], who found that the wave disintegration resembles the fission process characterized by Aghsaee et al [52] and Arthur and Fringer [54]. In our experiments, however, the shoaling processes occur periodically.…”

“…Although the mechanisms leading to the second-mode solitarylike waves differ, in both studies, the nonlinear internal waves have similar degeneration processes as they approach the sloping boundary. However, for the same bottom slope, s ≈ 3%, the second-mode nonlinear internal waves (in case 3) present a robust wave reflection, while the similar internal solitarylike waves in Carr et al [31] show no wave reflection. This last result suggests that the wind-driven baroclinic circulation might be crucial for supporting the periodic propagation of the nonlinear internal waves from side to side in the stratified basin.…”

“…In this scenario, internal waves degenerate along the slope, which enhances turbulence and vertical mixing. However, previous studies show that, as the slopes steepen, the degeneration of internal waves becomes weaker and waves can reflect more energy [31,52]. This implies less mixing and less dissipation of kinetic energy on the sloping boundaries [30,44].…”

“…Carr et al [31] investigated the shoaling of second-mode solitarylike waves via laboratory and numerical experiments generated using a lock-release method in a still, three-layer stratified fluid. By contrast, the second-mode nonlinear internal waves in case 3 (NL-V2H1) result from a periodic forcing, and they coexist with a wind-driven basin-scale circulation.…”

“…These cases are used to provide insights into how the horizontal transport is affected by changes in the vertical modal structure. Additionally, we examine a third case in which the V2H1 internal wave is affected by strong nonlinearities (NL) that resemble previous observations [e.g., 10,31]. We denote this case as NL-V2H1 [ Fig.…”