Nonlinear shoaling of shallow water waves: perspective in terms of the inverse scattering transform

Osborne, A. R.; Bergamasco, L.; Serio, M.; Bianco, Lucia Dal; Cavaleri, Luigi; Drago, Michele; Iovenitti, L.; Viezzoli, D.

doi:10.1007/bf02511838

Cited by 4 publications

(1 citation statement)

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“…Three parameters were used to assess the characteristics of the observed waves: the Ursell number, wave skewness, and wave asymmetry. The Ursell number [ Ursell , ] is a dimensionless parameter often used to quantify the nonlinearity of surface waves [e.g., Kirby and Dalrymple , ; Osborne et al , ; Peng et al ., ]. The local Ursell number, U , utilizes the horizontal and vertical extents of a wave (relative to water depth) and is defined as

U = \frac{H_{s} λ^{2}}{h^{3}}

where the wavelength, λ, was determined from the wave period.…”

Section: Methodsmentioning

confidence: 99%

Observations of wave transformation over a fringing coral reef and the importance of low‐frequency waves and offshore water levels to runup, overwash, and coastal flooding

2016

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Many low‐lying tropical islands are susceptible to sea level rise and often subjected to overwash and flooding during large wave events. To quantify wave dynamics and wave‐driven water levels on fringing coral reefs, a 5 month deployment of wave gauges and a current meter was conducted across two shore‐normal transects on Roi‐Namur Island in the Republic of the Marshall Islands. These observations captured two large wave events that had waves with maximum heights greater than 6 m with peak periods of 16 s over the fore reef. The larger event coincided with a peak spring tide, leading to energetic, highly skewed infragravity (0.04–0.004 Hz) and very low frequency (0.004–0.001 Hz) waves at the shoreline, which reached heights of 1.0 and 0.7 m, respectively. Water surface elevations, combined with wave runup, reached 3.7 m above the reef bed at the innermost reef flat adjacent to the toe of the beach, resulting in flooding of inland areas. This overwash occurred during a 3 h time window that coincided with high tide and maximum low‐frequency reef flat wave heights. The relatively low‐relief characteristics of this narrow reef flat may further drive shoreline amplification of low‐frequency waves due to resonance modes. These results (1) demonstrate how the coupling of high offshore water levels with low‐frequency reef flat wave energetics can lead to large impacts along fringing reef‐lined shorelines, such as island overwash, and (2) lend support to the hypothesis that predicted higher sea levels will lead to more frequent occurrences of these extreme events, negatively impacting coastal resources and infrastructure.

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