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Shoaling mode-2 internal solitary-like waves

Published online by Cambridge University Press:  02 October 2019

Magda Carr Open the ORCID record for Magda Carr [Opens in a new window] ,
Marek Stastna ,
Peter A. Davies  and
Koen J. van de Wal
Magda Carr*
Affiliation:
School of Mathematics, Statistics and Physics, Newcastle University, NE1 7RU, UK
Marek Stastna
Affiliation:
Department of Applied Mathematics, University of Waterloo, Ontario, N2L 3G1, Canada
Peter A. Davies
Affiliation:
Department of Civil Engineering, University of Dundee, DD1 4HN, UK
Koen J. van de Wal
Affiliation:
Eindhoven University of Technology, PO box 513, 5600MB Eindhoven, The Netherlands
*
†Email address for correspondence: magda.carr@ncl.ac.uk
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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.

JFM classification

Boundary Layers: Boundary layer separation Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 879 , 25 November 2019 , pp. 604 - 632
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Copyright
© 2019 Cambridge University Press 

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