ISWs and Slopes

Internal Solitary Waves are able to travel large distances without significantly changing. However, when they move over a slope they do change, undergoing one of four “breaking” processes, this process is known as shoaling. The processes that waves undergo under these scenarios are globally and locally important in the distribution of heat, nutrients and water masses.

The specific breaking process that a wave will undergo depends on it’s “wave steepness” (the wave amplitude / wavelength) and the steepness of the slope. The breaking processes we observe are similar to those we see for surface waves shoaling onto a beach, which also depend on similar quantities. Using laboratory experiments and numerical models of internal solitary waves propagating over a smooth straight slope, we found that the shape of the density profile also impacted the classification, specifically, stratification can prevent certain breaking types from forming.

Wave Surging

When the wave steepness is low (e.g. a very small amplitude wave), we get wave surging. Here the wave gives way to a small pulse of fluid that surges upslope ahead of the wave. This video is a false colour, raw image from the lab.

Wave Collapsing

This process happens for waves with medium wave steepness over medium slopes. As the wave passes, you can see immediately behind it on the bed, a flow reversal. A separation bubble forms and grows as the wave moves over the slope, and becomes unstable, forming a vortex (known as a global instability) that pulls the interface (pycnocline) back on itself.

Wave Plunging

For the steepest waves over steep slopes, plunging occurs. The speed of any wave in shallow water is proportional to the square root of it’s depth. Here, the wave’s speed is slowing down as it moves into shallower water, but the back of the wave (in deeper water) continues to move forward as the trough of the wave slows. This produces a plunging forward of the back of the wave, which overtakes the trough itself.

Wave Fission

A very different process occurs for internal solitary waves travelling over the gentlest slopes, named fission. Here, the wave of depression (the interface is displaced downward) gives way to a series of internal solitary waves of elevation (where the interface is displaced upward).

This work consisted of both laboratory experiments, and the SPINS numerical model (Subrich et al., 2013) to extend our experimental output further, and to gain a full suite of simultaneous measurements not available in the laboratory.

This work was published in Journal of Fluid Mechanics, and a paper focussed on the fissioning breaker type published in Environmental Fluid Mechanics.

Readers may also be interested in Carr et al. (2019)’s work on shoaling mode-2 Internal Solitary Waves Published in Journal of Fluid Mechanics