Coastal Creationism - Part 2: Complex curves
What are the fundamental shapes of epic reefs?
As we discussed in the last article, creating epic surfing reefs requires a lot of critical factors to come together by chance. However, when they do the result is a rare natural wonder - a perfect surf reef! Surfers know them by sight, and from an entire watery planet only a small selection of truly world class reefs seem to reappear in the photos, movies and webclips, each with very distinctive characteristics: Pipeline, P-Pass, Cloudbreak, Teahupoo, Mavericks, Trestles, The Right, North Point etc.
There are many reefs that can get really good but are not at that ‘world class’ level. They can be fickle, have slow sections, shut down or pinch closed too often. They may have some good waves, but not many “perfect” waves. However it seems that many of these good reef breaks are surrounded or close to other good reef breaks. The North Shore of Oahu is often described as the ‘7 Mile Miracle' because the density of quality reefs lined up one after the other along a short section of coast. Of course it also helps that the coast catches all the good swells from a variety of consistent swell windows and is offshore in the prevailing trade winds. Clearly there is something special that has shaped the undersea contours so that more often than not, swells are tripped up in to steeply plunging waves that peel at excellent angles.
Referring to the North Shore as the 7 Mile Miracle acknowledges the unlikeliness that Pipeline (First, Second,and Third Reefs), Backdoor, Off The Wall all occur in the space of a few hectares. Then of course there are all those other spots, Rocky Point, Sunset, Velzyland, Waimea Bay, Chuns, Jockos, Alligators, Laniakea, Haleiwa.
The 7 Mile Miracle is not just a function of swell and wind, it is also a geological marvel. The basalt lava flows spreading out from the the now extinct Oahu hot spot volcanoes were of just the right thickness and shape to result in convex shaped lozenges of rocky reef oriented at good peel angles to the prevailing swells. Nature has further contributed with coral reef growth and even occasional sand banks.
The lessons we have learned from Artificial Surfing Reef research is that reefs with flat gradients become less interesting with larger swells. That is, a reef or beach that is dipping at the same angle throughout the surf zone could produce good steep waves on smaller swells but it will produce fat, slow, spilling waves on bigger swells. This is because the plunging wave intensity is proportional to the beach steepness, i.e the steeper the gradient of the reef, the steeper the plunging wave.
However, of greater significance is that plunging wave intensity is also inversely proportional to the square root of the wave height (The Irribarren Number). This means that the bigger the wave the less intense (steep and hollow) the plunging wave for a given reef gradient. The period of the swell is also significant but we will leave this discussion for another time.
Based on the relationship between reef gradient and wave height a little bit of applied mathematics reveals that optimal reef shapes are convex. That is, they curve upwards with the steepest face of the reef in the deepest water, and the dip angle of the reef becoming flatter progressively into the shallower water.
Sketch of convex reef profile for an artificial surfing reef. Waves approach from the right (Image courtesy ASR)
As surfers well know, waves will bend around a reef, and as they do they trace the curves of the reef. The wrapping effect is caused by refraction - when waves travel faster in deeper water and slower in shallower water. In deeper water this can ‘lens’ the wave, magnifying wave heights resulting in some spots enjoying bigger and better waves than others (more on this later).
When we look at the section of the reef that is creating the breaking wave, the unbroken wave is still in deeper water and travelling faster than the breaking section, bending (wrapping) the unbroken wave toward the reef. This also has the effect of reducing the peel angle, creating a faster peeling section.
If we look at the ‘orthogonal’ of the wave as it breaks we are looking at the perpendicular to the breaking waves crest. If a swell wraps in toward the reef, then the orthogonal of the wave is actually a curve toward the shallowest part of the reef. So the convex shape of the reef is not based on a straight cross section; it is the water depth as the wave orthogonal curves toward the shallows.
Reef gemoetry is a complex interplay of curved surfaces that intersect with wave energy, and when describing it we run the risk of sounding like a bunch of shapers standing around talking about why their boards work (or don’t). Despite the different disciplines, there are many similarities as complex curves comprise the boards we ride and they also give shape to the waves themselves. In fact, some shapers are actually making the leap from shaping surfboards to actually shaping waves, such as the work of Webber Wave Pools.
(Image above is of the proposed artificial surfing reef for the City of Albany. It appears courtesy of Royal HaskoningDHV)
Coastal Creationsim is an eight part series written by Chris Buykx. Chris Buykx is a geologist, traveller and lifelong surfer. Specialising in eco-tourism, his passion is interpreting nature and the environment. Chris is a resident of Sydney’s Northern Beaches though he's currently doing a lap of Australia with his family. Read Part 1: Basic Reef Shapes