Effect of various forms currents on regular nonlinear waves in shallow water is investigated by use a computational fluid dynamics approach. A range wave conditions with different heights and periods are considered. three types these investigated, namely (i) uniform current over the depth, (ii) shear from seafloor to still-water level, (iii) custom profile that changes depth. The profiles consi...

This paper presents a new third-order trajectory solution in Lagrangian form for the water particles wave-current interaction flow based on an Euler–Lagrange transformation. The explicit parametric highlights of particle and wave kinematics above mean level within vertical column, which were calculated previously by approximation method using Eulerian approach. Mass transport associated with di...

The fully nonlinear and weakly dispersive Green-Naghdi equations for shallow water waves of large amplitude is studied. An hybrid finite volume and finite difference splitting approach is proposed. Numerical validations are then performed in one horizontal dimension.

Observations from a lander fixed to the seafloor over the continental shelf in 124 m of water provide highly-resolved velocity measurements through nonlinear internal waves of elevation. From these measurements we directly determine, for the first time, the nonhydrostatic pressure disturbance (pnh) in nonlinear internal waves. For near-bottom waves of elevation ranging in amplitude (a) from 12 ...

We derive a normal form of nonlinear equations for short equatorial waves considered in the framework of the rotating shallow water model. We show dynamical splitting of equatorial Rossby and inertia-gravity waves. We derive an effective Hamiltonian for the short inertia-gravity waves and consider their kinetics using the weak turbulence approach. Stationary power-law energy spectra are obtaine...

The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known ([PQ99] and [Pau03]) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We st...

We present a new hybrid asymptotic-numerical method to study nonlinear wave-body interaction in threedimensional water of arbitrary depth. After solving a simplified body problem numerically using a distribution of singularities along the body surface, we reduce the nonlinear free surface problem to a closed system of two nonlinear evolution equations, using a systematic asymptotic expansion, f...