A Curiosity of Cusps
It is often said that beauty is in the eye of the beholder. For me a trip to the beach is enhanced when I see cusps. These delightful, rhythmic features are often so captivating in their geometric perfection that one cannot help pondering on the forces of nature that creates (and destroys) them.
Much has been written about the origin of cusps. My first encounter as an undergraduate was reading Douglas Johnson’s incredible text on Shore Processes and Shoreline Development (1919). In the chapter on “Minor Shore Forms” he describes cusps as features built by wave action where “sand, gravel or coarse cobblestones are heaped together in rather uniformly spaced ridges that trend at right angles to the sea margin, tapering to a point near the water’s edge”. He adds that of minor forms on the shore zone, none has proved more puzzling than cuspate deposits. He reviewed various theories that were around in 19th and early 20th centuries. The earliest account he found was a paper on shingle beaches by Palmer in 1834 in which it was concluded that cusps were produced by waves driven directly upon the beach.
Around the time Johnson was writing, E.C. Andrews was observing beach formations over a 3-year period on Lady Robinsons Beach, Botany Bay (Journal of Royal Society of NSW, 1912, 158-185). Andrews, in this remarkable study, realised that one must understand the formation of the beach itself to appreciate the origin of cusps. While he concluded that cusps are due to the action of interfering waves, he was still aware that there is no consensus on their origin.
That cusps remain puzzling and continuing to attract attention can be seen in the paper by Almar et al. (2008, Marine Geology, 254, 216-233). They comment: “although the self-organizing theory provides a better fit to the data and theory [than subharmonic standing edge wave theory], we are unable to conclusively refute any of the mechanisms causing beach cusp formation”. Since Johnson’s 1919 review and Andrews 1912 paper, considerable effort has been undertaken in the field and laboratory to test hypotheses on cusp origin. Textbooks by Colin Woodroffe and by Gurd Masselink and Michael Hughes give summaries. Most papers refer to the pioneering work of Guza and Inman (1975) on the role of edge waves. Their research created a flurry of excitement about just what wave forces were operating on the beach face to produce cusps. Many tried to find (and surf) the edge waves as captured by Pat Hesp in his 1993 “review” in Journal of Coastal Research (15, 230-231; see below). This is not the place to go into details, but I must pay tribute to work by others in Australia such as Eliot, Masselink, Hughes, Turner, Short and Wright.
Ian Eliot once presented a paper (“Beach cusps on a sandy beach”, unpublished) at the ANZAAS Congress in Perth in 1973. It was based on his observations at Durras on the NSW south coast. I recently found a copy of his paper and was fascinated by his emphasis on wave action as a trigger mechanism for slope failure; he concluded that “beach cusps are thought to be more a reflection of slope failure than to differential sorting of sediment in the swash zone. However, the two processes are not regarded as being mutually exclusive”. The distinction between erosional and accretionary minor beach forms is more apparent when one examines his work.
My first field exposure to cusps took place at Shoal Bay near the entrance to Port Stephens. The year was 1960 and I was escorted by the late Peter McKenzie of rip current fame. He took me to the west end of this steep beach commenting that you will always find one or more sets of cusps at this location. Sure enough, my return visits have not disappointed me. At times I have observed a tiered set of cusps, the highest with the widest spacing and possibly erosional in origin, the lowest more closely spaced, rhythmic, symmetrical and accretionary. Similar features have been seen on other steep, coarse sand beaches in NSW, such as Pearl Beach studied by Masselink.
The arrival of Don Wright at Sydney University in 1974 stimulated great interest in beach dynamics. We were soon chasing edge waves on steep “reflective” beaches in the spirit of one of Don’s heroes, Bob Guza. This work was part of a much broader study of beach morphodynamics that incorporated long term beach observations and surf zone wave and current measurements (Wright et al., 1979, Marine Geology, 32, 105-140; Wright and Short, 1984, Marine Geology,56,93-118). It was a privilege to be part of the experiments that Don oversaw along with Peter Cowell and John Chappell. Andy Short continued the measurement tradition at Sydney in his supervision of PhDs. Many undergraduates participated in field experiments.
One memorable experience occurred in 1976 at a then reflective beach south of Batemans Bay (McKenzies also known as Bracken). As the students gathered in wet suits for offshore surveying, a group of cyclists arrived and immediately became to strip off. The leader of this group was the late Jim Cairns MP former Treasurer in the Whitlam Government. His “hippie” entourage was on tour of the east coast. Don and I decided that this was all too much for our students and abandoned our quest for edge waves and made them swim out to deeper waters to remove them from the sight of these naked folk. They soon left allowing us to return to teaching beach dynamics on a beach alive with beautiful cusps not bodies!
And so the quest for further understanding of cusps continues.
I would like to thank Andy Short for his help with this blog and the contribution of the cusp photograph, and Pat Hesp for permission to quote his insightful poem on edge waves and surfzone dynamics:
We were on the beach near Bulli when an edge wave passed us by, as we sat upon a dune and drank our beer, and as we watched in awe little cusps appeared upon the shore and all were filled with a strange exciting fear.
We waded down the tidal brook to get ourselves a closer look at this strange surf zone phenomena, someone cried, “My God! Its resonance, subharmonic excitance,” and he staggered off to have another at the bar.
“Its simple to explain”, said Don Wright with a grin. “Its just a little rascal that steals energy to begin, and then just like a mated sow, it grows and grows until somehow, it reaches equilibrium”.
There are many known frequencies such as an infragravity band, bumps and hollows, troughs and holes are formed where a wave guide is at hand; zero crossings of drift velocity occur at nodes and antinodes, and bars, rips, cusps and rhythmic cells generate from both bed and suspended loads.
So, you can take your simple airy wave and oscillatory bore, your tsunami and your set up and internal waves offshore, for I’d rather have an edge wave and beach face reflection, and a gradient in momentum flux in a shoreward direction.
Apart from where noted, words by Prof Bruce Thom. Please respect the author’s thoughts and reference appropriately: (c) ACS, 2019, for correspondence about this blog post please email firstname.lastname@example.org