Numerical study of transient nonlinear harbor resonance

Abstract

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...

Improvements on the normal mode decomposition method used in harbor resonance

“…It should be noted here that in the second step of the NMD method, the number of resonant modes with decomposed response amplitudes, that is, the parameter M in equation (14), must be determined in advance. In all numerical experiments in this article, M is set to 30.…”

Numerical investigation of infragravity wave amplifications during harbor oscillations influenced by variable offshore topography

“…Recently, Dong et al (2010b) carried out series of numerical experiments based on a fully nonlinear Boussinesq model, FUNWAVE 2.0, and adopted a wavelet-based bispectrum to investigate how the spectrum components of short wave groups take part in nonlinear wave-wave interactions during different phases of harbor resonance. The effects of short wave frequencies on the IG period components inside the harbor were also studied in that paper.…”

“…The effects of short wave frequencies on the IG period components inside the harbor were also studied in that paper. Similar to Dong et al (2010b), based on numerical simulations by the FUNWAVE 2.0 model, Dong et al (2013) proposed a wave analysis technique to decompose the IG period components inside the harbor into bound and free IG waves, and further studied the effect of the short wavelength on the bound and the free IG waves and their relative components inside the harbor when the lowest resonant mode, which is induced by bichromatic wave groups, occurs. Subsequently, Gao et al (2016a) expanded the studies of Dong et al (2013) in the following two aspects.…”

“…For the three papers mentioned above (i.e. Dong et al (2013); Dong et al (2010b); Gao et al (2016a)), the water depths inside and outside the harbor were set to a constant, and the influence of the offshore topography on harbor oscillations was not considered.…”

“…Thirdly, this paper systematically investigates the influences of the incident short wave amplitude on the maximum IG period component amplitude, the bound and free IG waves and their relative components inside the harbor. Identical to Dong et al (2013); Dong et al (2010b); Gao et al (2016a); Gao et al (2017b), all numerical experiments are performed using the FUNWAVE 2.0 model as well. For simplification, the harbor is assumed to be long and narrow, and then the free surface movement inside the harbor essentially becomes one dimensional.…”