Analytical study on long wave refraction over a dredge excavation pit

Niu, Xiaojing; Yu, Xiping

doi:10.1016/j.wavemoti.2010.11.001

Cited by 11 publications

(2 citation statements)

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“…7a). This problem was also studied by Niu and Yu (2011b) and Liao et al (2014), who derived an analytic solution for long wave refraction over a dredge excavation pit. Good agreement is obtained between the 2014) for α = 2 (see Fig.…”

Section: Verificationmentioning

confidence: 99%

Study on the Propagation and Focusing Mechanism of Long Waves over A Submerged Atoll

Liu

Zheng

et al. 2023

China Ocean Eng

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An analytical solution for long waves propagating over a submerged atoll is established. The atolls involved in this study are annular coral reefs with large lagoons in the middle, and the expression of the cross section is a trinomial function of the radial distance, i.e., h=ar2s−brs+h0, where s is the positive rational number. This analytical solution extends the theory by Wang et al. (2018) as s is no longer limited to s=2/m, where m is the positive integer. In addition, by adjusting the terrain parameters properly, the analytic solution can be degenerated to describe the wave propagation over topography with a hump or pit. According to the relationship between wave rays and wave energy, the distribution characteristics and formation mechanism of energy over the topography are expounded. When the lagoon is non-existent, all wave rays converge at the x-axis, which results in an abrupt amplification of the wave amplitude around the convergence point. When a lagoon is mounted on the top of the atoll, the rays are scattered due to the refraction of the lagoon, and only some rays converge at the symmetrical axis and the ridges on both sides, which results in the amplification of wave amplitudes in these areas.

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Section: Verificationmentioning

confidence: 99%

Study on the Propagation and Focusing Mechanism of Long Waves over A Submerged Atoll

Liu

Zheng

et al. 2023

China Ocean Eng

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“…Jung and Suh (2007) further extended their solution to a pit with water depth decreasing in proportion to an integer power of radial distance from the pit center. Niu and Yu (2011b) and Liao et al (2014) respectively derived analytic solutions of the mild-slope wave equation to describe wave propagation over an idealized axisymmetrical dredge excavation pit composed of a flat bottom and a convex slope.…”

Section: Introductionmentioning

confidence: 99%

Analytic study on long wave transformation over a seamount with a pit

Wang

Zheng

et al. 2018

Ocean Engineering

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In this paper, an analytic solution is derived for linear long waves scattering over a submarine seamount landform with a pit. The seamount is axisymmetric with a pit on the top. The water depth is defined by a trinomial function in the radial direction. The governing linear shallow water equation for long waves is expressed in the polar coordination, which is solved through separation of variables. As the topography is axisymmetric, solutions can be written as Fourier-cosine series. Waves over the seamount are expressed using Frobenius series expansion, while the water surface elevation in the outer region is expressed as Fourier-Bessel series, and the final solution is obtained by matching them at the conjunction. The solution can be degenerated into the previous analytic solutions for waves propagation over an axisymmetric pit or a submerged hump by adjusting the topography parameters.

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