Stratification effects on shoaling internal solitary waves

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.

Dense pulses formed from fissioning internal waves

“…These results for the surface stratification are qualitatively similar to the thin tanh stratification simulations in this study, as well as prior high resolution simulations of Xu and Stastna [19] and experimental observations of Ghassemi et al [28] for the thin tanh stratification. In addition, the dynamics are comparable to an experimental observation of the emergence of fissioning dynamics in the surface stratification [34].…”

“…Whilst the use of 3-D simulations in studies of internal wave shoaling would be desirable in order to resolve lobe-cleft instabilities and lateral variability, such simulations over this length of wave tank are too computationally expensive. Furthermore, past studies have highlighted the qualitative similarity of wave breaking in 2-D and 3-D simulations during the phases of shoaling studied here (the approach to the slope, breaking event, and start of up-slope propagation) [29,34,45]. Following on from these studies, it is expected that lateral variability and instabilities (which form only in 3-D simulations) would impact on the degeneration process of the pulses formed by fission.…”

“…ISWs were simulated in a rectangular tank with waves initiated using the lock gate technique, with the same simulation setup to the extended tank described in [34]. A schematic of the model set-up is given in Fig.…”

“…For example, the Labrador Sea is well represented by the three layer idealised system, whilst in the Sulu Sea, density varies linearly with depth over the entire upper layer, so a broader pycnocline is more representative [33]. Focusing on steeper slopes, previous work investigated the role of varying stratification on shoaling dynamics [34], identifying that dependent on the location of density gradients in the stratification, different shoaling behaviours were suppressed. Past studies of the field have also identified the role of seasonal variation in offshore stratification (as a result of upwelling) in influencing the behaviour of bores [35,36].…”

Interactions Between Internal Solitary Waves and Sea Ice

“…Various other scales can be applied to scale flows, the most commonly used are the Reynolds number, Re = UL / ν = cH / ν where U , L are indicative velocity (not float velocity as elsewhere in this paper) and length scales, here taken to be c and H respectively (formulation from Hartharn‐Evans et al., 2022). The Froude number, $$\mathrm{Fr}=U/\sqrt{gL}$$ is also a useful scaling term.…”