Abstract
This combined numerical/laboratory study investigates the effect of stratification form on the shoaling characteristics of internal solitary waves propagating over a smooth, linear topographic slope. Three stratification types are investigated, namely (i) thin tanh (homogeneous upper and lower layers separated by a thin pycnocline), (ii) surface stratification (linearly stratified layer overlaying a homogeneous lower layer) and (iii) broad tanh (continuous density gradient throughout the water column). It is found that the form of stratification affects the breaking type associated with the shoaling wave. In the thin tanh stratification, 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 $A_w/L_w$ for a given topographic slope, where $A_w$ and $L_w$ are incident wave amplitude and wavelength, respectively. In the surface stratification regime, the breaking classification differs from the thin tanh stratification. Plunging dynamics is 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, plunging dynamics is likewise inhibited and the near-bottom density gradient prevents the collapsing dynamics. 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 in the literature.
Highlights
Across the world’s oceans, variations in seawater temperature and salinity stratify the water column, producing conditions where density disturbances can propagate as internal waves
0 6.3 6.2 6.1 6.0 5.9 5.8 5.7 5.6 x (m) which have previously been identified in the literature in the thin tanh profile stratification (Sutherland et al 2013), are investigated for different stratification types
Slope and wave steepness are held fixed in the displayed collapsing (§ 4.3), plunging (§ 4.4) and surging in the broad tanh profile stratification (§ 4.5) examples shown, whilst the surging wave example (§ 4.2) in the surface stratification is for the same slope
Summary
Across the world’s oceans, variations in seawater temperature and salinity stratify the water column, producing conditions where density disturbances can propagate as internal waves. Internal solitary waves (ISWs) are a particular form of internal waves that have amplitude comparable to the pycnocline thickness, and often the overall depth of the water column (e.g. Grue et al 1999). They are characterised by a balance of nonlinear steepening and wave dispersion, and as a result are able to travel large distances without significant change of form or magnitude. Internal waves are generated on density interfaces in stably stratified fluids by barotropic motion over topography such as sills, slopes and the shelf edge Internal waves are generated on density interfaces in stably stratified fluids by barotropic motion over topography such as sills, slopes and the shelf edge (e.g. Grue 2005; da Silva, Buijsman & Magalhaes 2015; Rayson, Jones & Ivey 2019), with the evolution of the barotropic internal tide motion into far-field mode-1 and higher-mode ISWs being determined by nonlinear steepening mechanisms (Rayson et al 2019)
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