Fundamental singularities in the theory of water waves with surface tension

1970/06/01 by P. F. Rhodes-Robinson · 1 citation
Earth and Planetary Sciences · Engineering · Mathematics · #Acoustics #Classical mechanics #Coastal and Marine Dynamics #Constant (computer programming) #Geometry #Gravitational singularity #Harmonic #Harmonic function #Infinitesimal #Mathematical analysis #Mathematics #Multipole expansion #Ocean Waves and Remote Sensing #Optics #Physics #Quantum mechanics #Surface (topology) #Surface tension #Surface wave #Tension (geology) #Wave and Wind Energy Systems

paper · pdf · doi:10.1017/s0004972700042015

openalex publication_date 1970/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

In this paper the forms are obtained for the harmonic potential functions describing the fundamental wave-source and multipole singularities which pertain to the study of infinitesimal time-harmonic waves on the free surface of water when the effect of surface tension is included. Line and point singularities are considered for both the cases of infinite and finite constant depth of water. The method used is an extension of that which has been used to obtain these potentials in the absence of surface tension.

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