I construct a sandpile model for evolution of the energy spectrum of the water waves in finite basins. This model takes into account loss of resonant wave interactions in discrete Fourier space and restoration of these interactions at larger nonlinearity levels. For weak forcing, the waveaction spectrum takes a critical ω shape where the nonlinear resonance broadening overcomes the effect of th...

In this paper, a space-time least-squares finite-element method for the 2D nonlinear shallow-water equations (SWE) is developed. The method can easily handle complex geometry, bed slope (source term), and radiation boundary condition without any special treatment. Other advantages of the method include: high order approximations in space and time can easily be employed, no upwind scheme is need...

Creating and rendering realistic water is one of the most daunting tasks in computer graphics. Realistic rendering of water requires that the sunlight and skylight illumination are correct, the water surface is modeled accurately and that the light transport within water body is properly handled. This paper describes a method for wave generation on a water surface using a physically-based appro...

arises as the equation for solitary-wave solutions to a fifth-order long-wave equation for gravitycapillary water waves. Being Hamiltonian, reversible and depending upon two parameters, it shares the structure of the full steady water-wave problem. Moreover, all known analytical results for local bifurcations of solitary-wave solutions to the full water-wave problem have precise counterparts fo...

A shallow water spectral wave prediction model based on a numerical solution of the radiative transfer equation is presented. The model is second generation and uses a simple yet effective representation for the nonlinear source term. In addition, the model pays particular attention to the shallow water processes of refraction, shoaling, bottom friction, and wave breaking. The flexibility of th...

The uniqueness theorem is proved for the linearized problem describing radiation and scattering of time-harmonic water waves by a vertical shell having an arbitrary horizontal cross-section. The uniqueness holds for all frequencies, and various locations of the shell are possible: surface-piercing, totally immersed and bottom-standing. A version of integral equation technique is outlined for fi...

Broadband mid-to-high frequency (0.6-18 kHz) acoustic wave propagation in shallow coastal waters (< 20 m) is influenced by a variety of oceanographic conditions. Physical parameters such as temperature and salinity as well as hydrodynamic parameters such as surface waves, tide and current can influence amplitude and travel time of signal transmissions. In this paper a unique set of simultaneous...

We investigate theoretically and experimentally the capillary-gravity waves created by a small object moving steadily at the water-air interface along a circular trajectory. It is well established that, for straight uniform motion, no steady waves appear at velocities below the minimum phase velocity c(min)=23 cm s(-1). We demonstrate that no such velocity threshold exists for a steady circular...

Long's equation describes stationary flows to all orders of nonlinearity and dispersion. Dissipation is neglected. In this paper, Long's equation is used to attempt to model the propagation of a solibore -a train of internal waves in shallow water at the deepening phase of the internal tide. 1. The Solibore Phenomenon The internal tide in shallow water often has a sawtooth shape rather than a s...