The motion of water in contact with air is well described by the incompressible Euler equations in the fluid domain, combined with two boundary conditions on the free surface, i.e., the interface with air. In special, but still physically relevant cases, the equations of motion can be viewed as evolution equations for the free surface. These equations are commonly referred to as the water wave ...

In this paper, we present a new systematic method to obtain some discrete numerical models for incompressible free-surface flows. The method consists in first discretizing the Euler equations with respect to one variable, keeping the other ones unchanged and then performing an asymptotic analysis on the resulting system. For the sake of simplicity, we choose to illustrate this method in the con...

We derive transport equations for the propagation of water wave action in the presence of subsurface random flows. Using the Wigner distribution W(x, k, t) to represent the envelope of the wave amplitude at position x, time t contained in high frequency waves with wave vector k/ε (where ε is a small parameter compared to a characteristic distance of propagation), we describe surface wave transp...

The propagation of wave disturbances in water of uniform depth is discussed, accounting for both gravity and compressibility effects. In the linear theory, free-surface (gravity) waves are virtually decoupled from acoustic (compression) waves, as the sound speed in water far exceeds the maximum gravity wave phase speed. However, these two types of wave motion could exchange energy via resonant ...

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We formulate a general multiphase model representing water-bubble mixture fluid and multi-component bubble populations. An enhanced 2-DV VOF model with a k− turbulence closure is used to model the mixture fluid phase. The bubble phase is governed by the advection-diffusion equations of the gas molar concentration and bubble intensity for groups of bubbles with different sizes. The initial bubbl...

In this paper, we study the quasi-potential for a general class of damped semilinear stochastic wave equations. We show that as the density of the mass converges to zero, the infimum of the quasi-potential with respect to all possible velocities converges to the quasi-potential of the corresponding stochastic heat equation, that one obtains from the zero mass limit. This shows in particular tha...

A novel approach combining a two-fluid free surface solver and an efficient hybrid turbulence modelling technique has been presented for the simulation of breaking waves and their interaction with structures. The incompressible Navier-Stokes equations are solved by a cell centred finite volume method based on the artificial compressibility approach. The free surface (water/air interface) is tre...