Abstract:
A gas bubble rising steadily in a pure liquid otherwise at rest at a moderate
Weber number is, to a good approximation, of oblate spheroidal
shape. Previous analytical calculations of that shape at high Reynolds
numbers have ignored viscosity. This paper shows that if one includes
viscosity by incorporating Rayleigh's dissipation integral in Lagrange's
equations, then the speed of rise is that given by Moore, and the shape
is that found for inviscid flow by El Sawi using the virial integral and
by Benjamin using Hamiltonian theory.
