in cylindrical polar coordinates is derived. This is followed by a review of the current knowledge on analytical theories and numerical treatments of nonlinear diffraction of water waves by offshore cylindrical structures. A brief discussion is made on water waves incident on a circular harbor with a narrow gap. Special emphasis is given to the resonance phenomenon associated with this problem....

A substantial part of the energy of wake waves from high-speed ships sailing in shallow water is concentrated in nonlinear components which at times have a solitonic nature. Recent results of investigations into solitonic wave interactions within the framework of the Kadomtsev-Petviashvili equation and their implications for rogue wave theory are reviewed. A surface elevation four times as high...

The nonlinear Schrödinger equation (NLSE) is one of the most widely applicable equations in physical science, and is used to characterize nonlinear dispersive waves, plasmas, nonlinear optics, water waves, quantum computing, and the dynamics of molecules. In this talk, we present an accurate generalized finite-difference time-domain (G-FDTD) scheme for solving nonlinear Schrödinger equations. T...

Abstract. Very steep waves constitute an essentially nonlinear and complicated phenomenon. Inter-related experimental and theoretical efforts are thus required to gain a better understanding of their generation and propagation mechanisms. A nonlinear focusing process in which a single unidirectional steep wave emerges from an initially wide amplitudeand frequency-modulated wave group at a predi...

The nonlinear Schrödinger (NLS) equation is a popular and relatively simple model used extensively to describe the evolution of nonlinear water-wave groups. It is often applied in relation to the appearance of extremely steep (freak, or rogue) waves in the ocean. The limits of the applicability of the NLS equation, and in particular the relevance of the model to rogue waves, are examined here o...

Standing waves are a fundamental class of solutions of nonlinear wave equations with a spatial reflection symmetry, and they routinely arise in optical and oceanographic applications. At the linear level they are composed of two synchronized counterpropagating periodic traveling waves. At the nonlinear level, they can be defined abstractly by their symmetry properties. In this paper, general as...

The giant tsunami occurred in the Indian Ocean on 26th December 2004 pays attention to this natural phenomenon and the possibility to use the analytical methods. The given paper demonstrates the role of nonlinear effects in the computed dynamics of the tsunami waves in shallow seas and the applicability of the rigorous and approximated solutions of the nonlinear theory of water waves to explain...

Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to ...

We have compared the results from linear and nonlinear theories of the shallow-water equations applied to the South China Sea. Our results indicate that tsunami waves in the South China Sea can be modeled with linear theory. There is little difference in the probability predicted by nonlinear theory and that forecasted by linear treatment on tall waves, more than two meters high, which may impi...

Interacting ocean surface waves force water column pressure fluctuations with spectral peaks at the same frequencies of primary microseisms (PM), double-frequency microseisms (DF), and seismic hum. Prior treatment of nonlinear ocean wave interactions has focused on the DF pressure fluctuations which, in the presence of opposing waves, do not decay with depth and hence are dominant in deep water...