Long Wave Propagation, Shoaling and Run-Up in Nearshore Areas

Sriram, V.; Didenkulova, Ira; Schimmels, Stefan; Sergeeva, Anna; Goseberg, Nils

doi:10.9753/icce.v34.currents.20

Cited by 1 publication

(1 citation statement)

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“…Osborne, et al [59] had discussed the applicability of the KdV equation and indicated that it may be applicable only when the product of water depth and wave number is less than 1.14. While, a direct comparison between the results from FEM and KdV model is made by Sriram, et al [60,61] for simulating the propagation of solitary waves, where it is shown that good agreement is achieved if the Ursell number is small, otherwise the difference between the free surface simulated by using the FEM and KdV model becomes larger when the Ursell number increases. Later, it has been pointed out that the KdV equation failed to describe the spectrum evolution in the cases where Ursell number is large while wave steepness is small [56].…”

Section: Introductionmentioning

confidence: 99%

Numerical study on the quantitative error of the Korteweg–de Vries equation for modelling random waves on large scale in shallow water

Wang

Yan

et al. 2018

European Journal of Mechanics - B/Fluids

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The Korteweg-de Vries (KdV) equation is often adopted to simulate phase-resolved random waves on large scale in shallow water. It shows that the KdV equation is computationally efficient and can give sufficiently accurate results, but it is not always suitable and the error by using it cannot be predicted. This paper attempts to give the quantitative formulas for estimating the error of the statistics when simulating random waves in shallow water by using it. The formulas are obtained by fitting the errors of the KdV equation in comparison with the fully nonlinear model using the same initial condition based on the Wallops spectrum with a wide range of parameters. This paper also demonstrates how the formulas would be used, e.g., to estimate the error of the results by using the KdV model, or to justify its suitability for modelling random waves on large scale in shallow water.

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