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Jim Gunson and Graham Symonds


From in situ measurements taken over several sea-breeze cycles off a beach in southwest (SW) Australia, the evolution of the one-dimensional spectrum of wave energy is observed to have a distinctive spectral shape. During the land-breeze phase of the cycle, lower rates of dissipation of wave energy are seen at high frequencies compared to midrange frequencies above the remnant wind-sea peak. A simulation of waves was performed using the Simulating Waves Nearshore (SWAN) model and produced the same spectral evolution, by generating longshore modes, as seen in the observations. The performance of whitecapping schemes available in SWAN was assessed, and the Alves–Banner scheme was found to best simulate the observed growth and decay of the wave spectra. During the onshore phase of the sea-breeze cycle, local wave growth is duration limited, and during the offshore land-breeze phase, wave growth is fetch limited. From an examination of the modeled two-dimensional spectra it is found that quadruplet interactions play a key role in spreading high-frequency wave energy in frequency and direction space.

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Stephanie Contardo, Ryan J. Lowe, Jeff E. Hansen, Dirk P. Rijnsdorp, François Dufois, and Graham Symonds


Long waves are generated and transform when short-wave groups propagate into shallow water, but the generation and transformation processes are not fully understood. In this study we develop an analytical solution to the linearized shallow-water equations at the wave-group scale, which decomposes the long waves into a forced solution (a bound long wave) and free solutions (free long waves). The solution relies on the hypothesis that free long waves are continuously generated as short-wave groups propagate over a varying depth. We show that the superposition of free long waves and a bound long wave results in a shift of the phase between the short-wave group and the total long wave, as the depth decreases prior to short-wave breaking. While it is known that short-wave breaking leads to free-long-wave generation, through breakpoint forcing and bound-wave release mechanisms, we highlight the importance of an additional free-long-wave generation mechanism due to depth variations, in the absence of breaking. This mechanism is important because as free long waves of different origins combine, the total free-long-wave amplitude is dependent on their phase relationship. Our free and forced solutions are verified against a linear numerical model, and we show how our solution is consistent with prior theory that does not explicitly decouple free and forced motions. We also validate the results with data from a nonlinear phase-resolving numerical wave model and experimental measurements, demonstrating that our analytical model can explain trends observed in more complete representations of the hydrodynamics.

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