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.

<p>Shoaling is a key mechanism by which Internal Solitary Waves (ISWs) dissipate energy, induce mixing, and transport sediment. Past studies of shoaling ISWs in a three-layer stratification (with homogeneous upper and lower layers separated by a thin pycnocline layer) have identified a classification system where waves over the shallowest slopes undergo fission, whilst over steeper slopes, the breaking type changes from surging, through collapsing to plunging as a function of increasing internal Irribaren number (Ir) defined with the topographic slope, s, and the incident wave’s amplitude and wavelength, A<sub>w</sub> and L<sub>w </sub>respectively, as <img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.9fb46536f70067154311161/sdaolpUECMynit/12UGE&app=m&a=0&c=d84eaf790c6586a46ed8fca09040fcd7&ct=x&pn=gnp.elif&d=1" alt="" width="117" height="24">. Here, a combined numerical and laboratory study extends this prior work into new stratifications, representing the diversity of ocean structures across the world. Numerical results were able to successfully reproduce past studies in the three-layer stratification, and those in the two-layer stratification in the laboratory. Where a linear stratified layer overlays a homogeneous lower layer (two-layer stratification), it is found that plunging dynamics are inhibited by the density gradient throughout the upper layer, instead forming collapsing-type breakers. In numerical experiments, where the density gradient is continuous throughout the full water column (linear stratification), not only are the plunging dynamics inhibited, but the density gradient at the bottom boundary also prevents the formation of collapsing dynamics, instead all waves in this stratification either fission, or form surging breakers. Where the wave steepness is particularly high in the linear stratification, the upslope bolus formed by surging was unstable, and Kelvin-Helmholtz instabilities were observed on the upper boundary of the bolus, dynamics not previously observed in the literature. These results indicate the importance of using representative stratifications in laboratory and numerical studies of ISW behaviours.</p>

<p>Internal Waves are commonly observed along density interfaces across the world’s oceans. In the Arctic Ocean, the internal wave field is much less energetic than at lower latitudes, but due to relative quiescence of the region, nonlinear internal waves are particularly important for mixing there. This mixing is responsible for bringing heat from warm Atlantic Water at intermediate depth towards the surface where it has ramifications for the formation and melt of sea ice, as well as the general circulation of the Arctic Ocean. In the rapidly changing Arctic Ocean, as sea ice extent declines, understanding how internal waves interact with sea ice, and how sea ice affects them is crucial, particularly in the marginal ice zone.</p><p>Using laboratory experiments of internal solitary waves (ISWs) propagating under model ice the interaction of ice and internal solitary waves is investigated. Specifically, (i) Particle Tracking Velocimetry is used to measure the motion of floating discs (with the same density as sea ice ρ = 910kg/m³), to determine how ice moves in response to the near-surface internal wave-induced flow using is quantified. Additionally, (ii) Particle Image Velocimetry is used to determine how the near-surface internal wave-induced flow dynamics are impacted by the presence and motion of the model sea-ice, which acts as a rough upper boundary condition and moves with the flow.</p>

Cold pulses generated by the fission of internal solitary waves over gentle slopes are an important source of nutrients and relief from excess heat to benthic ecosystems. This numerical study investigates the effect of stratification form on pulses produced by fission of internal solitary waves propagating over a smooth, gentle, linear topographic slope in 2D simulations. 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). Incident wave amplitude was varied. In the thin tanh stratification, good agreement is seen with past studies, whilst the dynamics observed in the surface stratification are very similar to those in the thin tanh stratification. However, in the broad tanh stratification, due to the different form of incident waves, the fission dynamics differ, but produce pulses similar in form to those produced by fission in the other stratifications. Pulse amplitude, wavelength and propagation velocity are found to strongly depend on incident wave amplitude, and each degenerate linearly as the pulse propagates upslope.