A NEW LIMITING FORM FOR STEADY PERIODIC GRAVITY-WAVES WITH SURFACE-TENSION ON DEEP-WATER

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.