M. Debiane et C. Kharif, A NEW LIMITING FORM FOR STEADY PERIODIC GRAVITY-WAVES WITH SURFACE-TENSION ON DEEP-WATER, Physics of fluids, 8(10), 1996, pp. 2780-2782
The method developed by Longuet-Higgins [J. Inst. Math. Appl. 22, 261
(1978)] for the computation of pure gravity waves is extended to capil
lary-gravity waves in deep water. Surface tension provides an addition
al term in the identities between the Fourier coefficients in Stokes'
expansion. This term is then 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 by using the Newton's
method. A new family of limiting profiles of steady gravity waves wit
h surface tension is found. (C) 1996 American Institute of Physics.