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Mark L. Buckley
,
Ryan J. Lowe
,
Jeff E. Hansen
, and
Ap R. Van Dongeren

Abstract

The effect of bottom roughness on setup dynamics was investigated using high-resolution observations across a laboratory fringing reef profile with roughness elements scaled to mimic the frictional wave dissipation of a coral reef. Results with roughness were compared with smooth bottom runs across 16 offshore wave and still water level conditions. The time-averaged and depth-integrated force balance was evaluated from observations collected at 17 locations along the flume and consisted of cross-shore pressure and radiation stress gradients whose sum was balanced by quadratic mean bottom stresses. The introduction of roughness had two primary effects. First, for runs with roughness, frictional wave dissipation occurred on the reef slope offshore of the breakpoint, reducing wave heights prior to wave breaking. Second, offshore-directed mean bottom stresses were generated by the interaction of the combined wave–current velocity field with the roughness elements. These two mechanisms acted counter to one another. Frictional wave dissipation resulted in radiation stress gradients that were predicted to generate 18% (on average) less setup on the reef flat for rough runs than for smooth runs when neglecting mean bottom stresses. However, mean bottom stresses increased the predicted setup by 16% on average for runs with roughness. As a result, setup on the reef flat was comparable (7% mean difference) between corresponding rough and smooth runs. These findings are used to assess prior results from numerical modeling studies of reefs and also to discuss the broader implications for how large roughness influences setup dynamics in the nearshore zone.

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Mark L. Buckley
,
Ryan J. Lowe
,
Jeff E. Hansen
, and
Ap R. Van Dongeren

Abstract

High-resolution observations from a 55-m-long wave flume were used to investigate the dynamics of wave setup over a steeply sloping reef profile with a bathymetry representative of many fringing coral reefs. The 16 runs incorporating a wide range of offshore wave conditions and still water levels were conducted using a 1:36 scaled fringing reef, with a 1:5 slope reef leading to a wide and shallow reef flat. Wave setdown and setup observations measured at 17 locations across the fringing reef were compared with a theoretical balance between the local cross-shore pressure and wave radiation stress gradients. This study found that when radiation stress gradients were calculated from observations of the radiation stress derived from linear wave theory, both wave setdown and setup were underpredicted for the majority of wave and water level conditions tested. These underpredictions were most pronounced for cases with larger wave heights and lower still water levels (i.e., cases with the greatest setdown and setup). Inaccuracies in the predicted setdown and setup were improved by including a wave-roller model, which provides a correction to the kinetic energy predicted by linear wave theory for breaking waves and produces a spatial delay in the wave forcing that was consistent with the observations.

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

Abstract

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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