The effect of surface tension on the progressive waves due to incomplete vertical wave-makers in water of infinite depth

Abstract

In this paper the influence of surface tension is allowed for in deriving formulas that determine the velocity potentials describing the outgoing progressive waves for two-dimensional time-harmonic motion due to both partially immersed and completely submerged vertical wave-makers in water of infinite depth. For this purpose an effective reduction method is developed to extend a known method suitable only in the absence of surface tension. The two results are used to find the reflected and transmitted waves due to waves incident upon partially immersed and completely submerged fixed vertical barriers, after reformulation as wave-maker problems; and to find the outgoing waves due to a partially immersed vertical hinged plate as a standard example. Certain edge-slope constants needed for the partially immersed wave-maker problem are evaluated using an appropriate dynamical edge condition.