Abstract
This note describes some quasi-analytical solutions for wave propagation in free surface Euler equations and linearized Euler equations. The obtained solutions vary from a sinusoidal form to a form with singularities. They allow a numerical validation of the free-surface Euler codes.
Highlights
This note describes some quasi-analytical solutions for wave propagation in free surface Euler equations and linearized Euler equations
The water wave problem described by the Euler equations with a free surface has been widely studied in the literature, see e.g. [5, 8, 10,11,12]
This paper proposes some quasi-analytical solution of these equations that allow, for example, to validate the efficiency of the numerical tools
Summary
The water wave problem described by the Euler equations with a free surface has been widely studied in the literature, see e.g. [5, 8, 10,11,12]. We consider the Euler system and the linearized Euler system over a flat bottom for x ∈ R and 0 ≤ z ≤ h(t , x) given respectively by (1)-(3) and (4)-(6), where u(t , x, z), w(t , x, z) are the two components of the velocity in the (x, z) domain, h(t , x) is the water depth, p(t , x, z) is the pressure and ρ0 is the density assumed to be constant: These systems are completed by initial conditions u(0, x, z) = u0(x, z), w (0, x, z) = w 0(x, z), p(0, x, z) = p0(x, z) , a dynamic boundary condition at the free surface ps = p(t , x, h(t , x)) = pa(t , x),.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
