Numerical study of transient nonlinear harbor resonance

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.

[1]  Jurjen A. Battjes,et al.  Seiche characteristics of Rotterdam Harbour , 2004 .

[2]  Paolo De Girolamo,et al.  An experiment on harbour resonance induced by incident regular waves and irregular short waves , 1996 .

[3]  Chiang C. Mei,et al.  Long-period oscillations in a harbour induced by incident short waves , 1989, Journal of Fluid Mechanics.

[4]  Philip L.-F. Liu,et al.  Finite-Element Model for Modified Boussinesq Equations. II: Applications to Nonlinear Harbor Oscillations , 2004 .

[5]  P. Liu,et al.  Harbour excitations by incident wave groups , 1990, Journal of Fluid Mechanics.

[6]  Harry B. Bingham,et al.  A new Boussinesq method for fully nonlinear waves from shallow to deep water , 2002, Journal of Fluid Mechanics.

[7]  Inigo J. Losada,et al.  Numerical modeling of nonlinear resonance of semi-enclosed water bodies: Description and experimental validation , 2008 .

[8]  Robert A. Dalrymple,et al.  A fully nonlinear Boussinesq model in generalized curvilinear coordinates , 2001 .

[9]  Michele Mossa,et al.  The FUNWAVE model application and its validation using laboratory data , 2009 .

[10]  D. Peregrine.  Long waves on a beach , 1967, Journal of Fluid Mechanics.

[11]  G. Dong,et al.  Experimental study of wave–wave nonlinear interactions using the wavelet-based bicoherence , 2008 .

[12]  Giorgio Bellotti,et al.  Transient response of harbours to long waves under resonance conditions , 2007 .

[13]  B. Bornhold,et al.  The landslide tsunami of November 3, 1994, Skagway Harbor, Alaska , 1996 .

[14]  G. Wei,et al.  A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves , 1995, Journal of Fluid Mechanics.

[15]  I. Losada,et al.  EXPERIMENTAL ANALYSIS OF LONG WAVES AT HARBOUR ENTRANCES , 2005 .

[16]  O. Nwogu.  Alternative form of Boussinesq equations for nearshore wave propagation , 1993 .

[17]  F. Raichlen,et al.  Nonlinear Oscillations in Rectangular Tanks , 1988 .

[18]  Ge Wei,et al.  A fully nonlinear Boussinesq model for surface waves. Part 2. Extension to O(kh)4 , 2000, Journal of Fluid Mechanics.

[19]  Chiang C. Mei,et al.  Nonlinear resonant excitation of a long and narrow bay , 1978, Journal of Fluid Mechanics.

[20]  Numerical modeling of surf beat generated by moving breakpoint , 2009 .

[21]  S. Elgar,et al.  Nonlinear Dispersion of Surface Gravity Waves in Shallow Water , 2002 .

[22]  Stanisław Ryszard Massel,et al.  Wavelet analysis for processing of ocean surface wave records , 2001 .