This Matlab code computes irrotational 2D periodic steady surface pure gravity waves of arbitrary length in arbitrary depth. The formulation is based on the so-called Babenko equation and pseudo-spectral discretization in the conformal domain. The resulting equation is solved using Petviashvili iteration method.

MANDATORY INPUT PARAMETERS:

• kd = k*d : relative depth (wavenumber "k" times mean water depth "d").
• kH2 = k*H/2 : steepness (half the total wave height "H" times the wavenumber "k").

OPTIONAL INPUT PARAMETERS:

• N : number of positive Fourier modes (default, N=2048).
• tol : tolerance (default, tol=1e-14).

OUTPUT PARAMETERS:

• zs = complex abscissas at the free surface (at the computational nodes).
• ws = complex velocity at the free surface (at the computational nodes).
• PP = Physical Parameters: PP(1)=depth, PP(2)=wavenumber, PP(3)=wavelenght,
• PP(4)=celerity c_e, PP(5)=celerity c_s, PP(6)=Bernoulli constant,
• PP(7)=crest height, PP(8)=trough height, PP(9)=impulse,
• PP(10)=potential energy, pp(11)=kinetic energy, PP(12)=radiation stress,
• PP(13)=momentum flux, PP(14)=energy flux, PP(16)=group velocity.

For more information on the method, please, read our preprint:

• D. Clamond & D. Dutykh. Accurate fast computation of steady two-dimensional surface gravity waves in arbitrary depth. Submitted, 2017