# Shoaling mode-2 internal solitary-like waves

Magda Carr, Marek Stastna, Peter A. Davies, Koen J. van de Wal

Research output: Contribution to journalArticlepeer-review

## 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.
Original language English 604-632 29 Journal of Fluid Mechanics 879 2 Oct 2019 https://doi.org/10.1017/jfm.2019.671 Published - 25 Nov 2019

## Fingerprint

Dive into the research topics of 'Shoaling mode-2 internal solitary-like waves'. Together they form a unique fingerprint.
• ### Davies, Peter

Person: Honorary