M. Debiane et C. Kharif, A NEW WAY FOR THE CALCULATION OF STEADY PERIODIC CAPILLARY-GRAVITY WAVES ON DEEP-WATER, European journal of mechanics. B, Fluids, 16(2), 1997, pp. 257-275
The method developed by Longuet-Higgins (1978) for the calculation of
steady gravity waves is extended to steady capillary-gravity waves in
deep water. Introduction of surface tension provides an additional ter
m in the quadratic identities between the Fourier coefficients in Stok
es's expansion. This term is reduced to a simple function of the slope
of the local tangent to the profile of the free surface. A set of non
linear algebraic equations is derived and solved using Newton's method
. Good agreement is found between the present results and those given
by previous methods. Limiting profiles of gravity-like waves are accur
ately calculated and a new family of limiting gravity waves is found.