Influence of surface tension on the propagation of axisymmetric waves

Abstract

A linearized theory of transient development of axisymmetric surface wave phenomenon in an inviscid, incompressible and homogeneous fluid due to an arbitrary oscillating pressure distribution acting on the undisturbed free surface of the fluid, including the effect of surface tension, is presented in this paper. The joint Laplace-Hankel transformations together with asymptotic methods are utilized to obtain the solutions of the free surface elevation for fluids of finite, infinite and shallow depth. It is shown that the solution consists of both the steady state and the transient components which are independently modified by surface tension. The transient motion decays to zero more rapidly due to the presence of surface tension than in the case when surface tension is neglected. Consequently, the steady state is attained in the limit ι → ∞. The effect of surface tension on the principal features of the axisymmetric wave motions is determined. It is shown that the principal influence of surface tension is to increase the phase and group velocity of the waves and make the energy more readily distributed among the rapidly travelling axisymmetric waves. Finally, it is found that this analysis is in perfect agreement with the corresponding analysis without surface tension.