Pointed bubbles rising in a two-dimensional tube

This document considers a periodic array of plane bubbles rising in a gravity field. This configuration can serve as a model for an advanced stage of Rayleigh-Taylor instability. Vanden-Broeck solved the problem numerically and showed that two classes of solutions are possible. One class is characterized by a bubble profile with a continuous slope at the apex of the bubble whereas the other is characterized by the presence of a cusp at the apex. In a recent paper Garabedian and Modi conjectured that solutions with a 120 deg. angle at the apex might also exist. In this paper a scheme is presented to compute such solutions. It is found that a solution exists at a unique Froude number of 0.36. This result does not support Garabedian's conjecture that bubbles with a 120 deg. angle at the apex exist for all values of F between 0.23 and 0.36.