Thesis (PhD)--University of South Australia, 2001. Includes bibliographical references (pages 225-232) In this dissertation, partial differential equations are derived which model the effect of sinusoidal, vertical forcing upon the surface of an infinitely deep, incompressible and quasi-irrotational (weakly vortical) fluid confined between two vertical walls. The model incorporates realistic physical effects such as surface tension acting along the interface between the fluid and the outside atmosphere, the dissipative nature of viscosity acting within the fluid, and the effect of weak vorticity induced by disturbing the fluid from ideal irrotational flow. A problem with similar models of weak vorticity is that they produce non-physical modes of oscillation which increase in energy. In contrast,this model is shown, both theoretically and numerically, to produce only modes which conserve or dissipate energy.The veracity and ramifications of the model are studied by analysing the behaviour of small-amplitude perturbations to an otherwise undisturbed surface. The theoretical analysis is accomplished using variational perturbation theory. The framework of this theory is substantially developed in this dissertation from generalised Taylor expansions using Fréchet derivatives. Whilst similar methods have been used elsewhere, mostlyon an ad hoc basis, I believe much of this work to be newly applied to this problem. Ihave also attempted to formulate a systematic methodology.