New nonlinear evolution equations are derived that generalize those presented in a Letter by Matsuno [Phys. Rev. Lett. 69, 609 (1992)]] and a terrain-following Boussinesq system recently deduced by Nachbin [SIAM J Appl. Math. 63, 905 (2003)]]. The regime considers finite-amplitude surface gravity waves on a two-dimensional incompressible and inviscid fluid of, highly variable, finite depth. A F...

The intrusion of a constant density fluid at the interface of a two-layer fluid is considered. Numerical solutions are computed for a model of a steady intrusion resulting from flow down a bank and across a broad lake or reservoir. The incoming fluid is homogeneous and spreads across the lake at its level of neutral buoyancy. Solutions are obtained for a range of different inflow angles, flow r...

The performances of phase-averaged parametric nearshore wave transformation models depend significantly on a reliable estimate the breaker index γ (the height-to-depth ratio), free model parameter that essentially controls amount breaking energy dissipation. While previous studies have suggested separate relationships between and offshore steepness (s0) or normalized local water depth (kh), par...

By performing two parallel numerical experiments-solving the dynamical Hamiltonian equations and solving the Hasselmann kinetic equation-we examined the applicability of the theory of weak turbulence to the description of the time evolution of an ensemble of free surface waves (a swell) on deep water. We observed qualitative coincidence of the results. To achieve quantitative coincidence, we au...

A stability of nearly limiting Stokes waves to superharmonic perturbations is considered numerically in approximation an infinite depth. Investigation the properties can give one insight into evolution wave. The new, previously inaccessible branches instability were investigated. Our numerical simulations suggest that eigenvalues linearized dynamical equations, corresponding unstable modes, app...

Waves on the submerged sloping seabed tend to transform and even break, inducing response exerting force shallowly-buried pipeline. In this study, a series of flume tests were carried out characterize wave propagation sandy seabed. Subsequently, considering pipeline burial effect ensuing investigated. Experimental results indicate that varies drastically seabed, accompanied with nonlinearity st...

Direct numerical simulation is used to study the turbulent flow over a smooth wavy wall undergoing transverse motion in the form of a streamwise travelling wave. The Reynolds number based on the mean velocity U of the external flow and wall motion wavelength λ is 10 170; the wave steepness is 2πa/λ = 0.25 where a is the travelling wave amplitude. A key parameter for this problem is the ratio of...

The effect of randomness on the stability of deep water surface gravity waves in the presence of a thin thermocline is studied. A previously derived fourth order nonlinear evolution equation is used to find a spectral transport equation for a narrow band of surface gravity wave trains. This equation is used to study the stability of an initially homogeneous Lorentz shape of spectrum to small lo...

This work investigates the extent to which potential vorticity gradients affect the vertical propagation of planetary-scale Rossby waves on the edge of a stratospheric polar vortex and their eventual nonlinear saturation and breaking. Using two different numerical modeling approaches, it is shown that wave propagation and wave breaking are significantly reduced when the potential vorticity grad...