 
Summary: The effect of surface tension on trapped modes
in waterwave problems
BY ROBERT HARTER, I. DAVID ABRAHAMS* AND MICHAEL J. SIMON
School of Mathematics, The University of Manchester, Oxford Road,
Manchester M13 9PL, UK
In this paper the effect of surface tension is considered on two twodimensional water
wave problems involving pairs of immersed bodies. Both models, having fluid of infinite
depth, support localized oscillations, or trapped modes, when capillary effects are
excluded. The first pair of bodies is surfacepiercing whereas the second pair is fully
submerged. In the former case it is shown that the qualitative nature of the streamline
shape is unaffected by the addition of surface tension in the free surface condition, no
matter how large this parameter becomes. The main objective of this paper, however, is
to study the submerged body problem. For this case it is found, by contrast, that there
exists a critical value of the surface tension above which it is no longer possible to
produce a completely submerged pair of bodies which support trapped modes. This
critical value varies as a function of the separation of the two bodies. It can be inferred
from this that surface tension does not always play a qualitatively irrelevant role in the
linear waterwave problem.
Keywords: water waves; trapped modes; surface tension; submerged body;
localized oscillations
