Surf’s Up: How the Seafloor Shapes Breaking Waves

A new study spearheaded by surfing scientists with Scripps Institution of Oceanography at UC San Diego revealed the physical relationships underlying a pattern familiar to generations of surfers.

Scripps PhD student Kanoa Pick and Scripps oceanographer Falk Feddersen led the research, which takes a closer look at what happens when waves approach the shore and begin to break. The study was published July 27 in the Journal of Fluid Mechanics.

“Surfers are incredibly observant,” said Pick, the lead author on the study. “They learn to recognize how changes in the swell and seafloor affect a wave, even if they don’t express those relationships through equations. Science gives us a way to test that intuition and quantify the physics behind it.”

While waves are often broadly classified as either “spilling” or “plunging” breakers, the researchers wanted to understand more precisely how the shape of a breaking wave changes depending on the slope of the seafloor and the wave’s offshore height, and what those changes mean for turbulence and sand transport.

Using a two-dimensional, fully nonlinear potential flow model, the researchers simulated solitary waves shoaling and overturning across a range of seafloor slopes and wave heights. Shoaling occurs when waves enter shallower water and grow taller. They found that steeper slopes produce larger, more horizontally oriented overturning waves with thicker jets of water projecting from the crest, while gentler slopes produce smaller, more inclined overturns with thinner jets.

The researchers discovered how to predict the size, shape, and orientation of an overturning wave with knowledge of the seafloor slope and offshore wave height. These predictions included the size of the overturn (i.e., barrel) and its projecting jet, as well as the overturn aspect ratio and angle. This goes beyond classifying waves as simply spilling or plunging by describing the precise geometry of how they break.

The researchers also connected the shape of a breaking wave to how quickly it steepens as it moves into shallower water. More rapid wave steepening produced larger overturns and jets with greater potential energy. This is important because when the overturning jet impacts the water’s surface, its potential energy is rapidly converted into turbulence and bubbles. Pick and Feddersen found that jet potential energy is strongly related to jet size, linking the geometry of a breaking wave to the turbulence generated as it breaks. That turbulence is a key driver of processes such as sand suspension and transport in the surf zone.

Overall, the work provides a more detailed framework for understanding how the seafloor and incoming wave characteristics shape breaking waves, and, in turn, how those waves generate the turbulence that helps move sand along the coast.

The study was funded by the Mark Walk Wolfinger Foundation. Feddersen noted key support for the research from the Mark “Marko” Walk Wolfinger Surfzone Research Fund. The fund was created by the Wolfinger family to honor the memory of Marko, an avid surfer from La Jolla, Calif.