Numerical modeling of nonlinear resonance of semi-enclosed water bodies: Description and experimental validation

Losada, Íñigo J.; González-Ondina, José M.; Diaz-Hernandez, Gabriel; González, M.

doi:10.1016/j.coastaleng.2007.06.002

Cited by 64 publications

(32 citation statements)

References 20 publications

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“…For a discussion of the quality of the results of this model (using a slightly different stabilization scheme), see [22]. The examples in this paper are more oriented to the comparison of the improvements of the stabilized formulation over the non-stabilized one (where the stabilization parameter is considered to be zero).…”

Section: Numerical Examplesmentioning

confidence: 99%

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Finite element approximation of the modified Boussinesq equations using a stabilized formulation

Codina

González-Ondina

Diaz-Hernandez

et al. 2008

Numerical Methods in Fluids

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SUMMARYIn this work, we present a finite element model to approximate the modified Boussinesq equations. The objective is to deal with the major problem associated with this system of equations, namely, the need to use stable velocity-depth interpolations, which can be overcome by the use of a stabilization technique. The one described in this paper is based on the splitting of the unknowns into their finite element component and the remainder, which we call the subgrid scale. We also discuss the treatment of high-order derivatives of the mathematical model and describe the time integration scheme.

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Section: Numerical Examplesmentioning

confidence: 99%

“…The sponge layer uses a simple Newtonian cooling scheme to dissipate energy, consisting of adding a force proportional to the velocity and in the opposite direction (see [6,10,22]). Continuous line is the model with the non-stabilized equations.…”

Section: Real Case: Lastres Harbormentioning

confidence: 99%

Finite element approximation of the modified Boussinesq equations using a stabilized formulation

Codina

González-Ondina

Diaz-Hernandez

et al. 2008

Numerical Methods in Fluids

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“…In order to flexibly fit the complex geometries of harbors and increase the computational accuracy, Woo and Liu [10] and Losada et al [11] developed numerical models for harbor resonance with the unstructured finite element method to Boussinesq equations.…”

Section: Harbor Resonance Infragravity Waves Wavelet-based Bispectrmentioning

confidence: 99%

Numerical study of transient nonlinear harbor resonance

Dong

Wang

et al. 2010

Sci. China Technol. Sci.

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It is generally accepted that nonlinear wave-wave interactions play an important role in harbor resonance. Nevertheless it is not clear how waves take part in those interactions. The aim of this paper is to investigate those processes for a rectangular harbor at transient phases. Long-period oscillations excited by bichromatic waves are simulated by the Boussinesq model. The simulations start from calm conditions for the purpose of studying the response process. The internal wavemaker stops working after the oscillations have reached a quasi-steady state, and it is used to simulate the damp process. In order to analyze temporary features of wave-wave interactions in different states, the wavelet-based bispectrum is employed. The influence of the short wave frequencies on long-period oscillations is investigated, and reasons are tried to be given from nonlinear triad interactions between different wave components and the interaction of short waves and the bay entrance. Finally, the response time and the damp time are estimated by a simple method. harbor resonance, infragravity waves, wavelet-based bispectrum, wave-wave interactionsCitation: Dong G H, Wang G, Ma X Z, et al. Numerical study of transient nonlinear harbor resonance.When ocean waves of certain periods come into a harbor opening, they are often trapped and amplified. The phenomenon of such external energy trapped in a semi-enclosed domain and exciting large oscillations is called harbor resonance. Harbor oscillations are excited by the resonance that results from the agreement of frequencies of incident waves and the natural frequencies of the harbor. These large-amplitude oscillations could break mooring lines, damage fenders, cause hazards in berthing and loading, navigation through the entrance, etc. For many harbors, the most important natural modes have rather long periods, ranging from several minutes to an hour. Tsunamis and moves or fluctuations of atmospheric pressure have been shown to drive these oscillations [1,2]. The primary energy source for the occurrence of long-period waves in the coastal region is the nonlinear interactions of short-period waves. Low-frequency waves are generated following the propagation of these short waves. Mei and Agnon [3] and Wu and Liu [4] used different algebraic methods to show that long-period oscillations can be excited by the incident group of short waves. Not only the bound long waves can be amplified inside the harbor, but also the free long waves will be released when short wave groups propagate through the entrance. Such free long waves can further resonate the natural modes of the harbor basin. These conclusions were supported by De Girolamo [5] in the laboratory.During the last decade, Boussinesq-type equations with improved dispersion characteristics and nonlinear properties have traditionally been solved, and applied to model wave propagation from nearly deep water to the shoreline [6−9]. In order to flexibly fit the complex geometries of harbors and increase the computational accuracy, Woo and Liu...

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“…To simulate such a phenomenon, some numerical models have been developed, including linear ones based essentially on mild-slope equations [1][2][3] and nonlinear ones based on Boussinesq-type models [4][5][6][7][8]. For reproducing short wave disturbances in harbors, the linear models are convenient with their computational efficiency and can be applied to relatively large domains.…”

Section: Introductionmentioning

confidence: 99%

An analytical investigation for oscillations in a harbor of a parabolic bottom

2016

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Based on the linear shallow water approximation, longitudinal and transverse oscillations in a rectangular harbor with a parabolic bottom are analyzed. The longitudinal ones are combinations of the Legendre functions of the first and second kinds and the transverse ones are expressed with modified Bessel equations. Analytic results for longitudinal oscillations show that the augmentation of rapidity of variation of the water depth shifts the resonant wave frequencies to larger values and slightly changes the positions of the nodes for the resonant modes. For the transverse oscillations trapped within the harbor which are typically standing edge waves, the dispersion relationship is derived and the spatial structures of the first four modes are presented. The solutions illustrate that all the trapped modes are affected by the varying water depth parameters, especially for the higher modes whose profiles extend farther and the distribution of the energy of transverse oscillations is influenced by the rapidity of variation of the bottom within the harbor.

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Numerical modeling of nonlinear resonance of semi-enclosed water bodies: Description and experimental validation

Cited by 64 publications

References 20 publications

Finite element approximation of the modified Boussinesq equations using a stabilized formulation

Finite element approximation of the modified Boussinesq equations using a stabilized formulation

Numerical study of transient nonlinear harbor resonance

An analytical investigation for oscillations in a harbor of a parabolic bottom

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