Bubble shapes in steady axisymmetric flows at intermediate Reynolds number

The shape of a gas bubble which rises through a quiescent incompressible, Newtonian fluid at intermediate Reynolds numbers is considered. Exact numerical solutions for the velocity and pressure fields, as well as the bubble shape, are obtained using finite difference techniques and a numerically generated transformation to an orthogonal, boundary-fitted coordinate system. No restriction is placed on the allowable magnitude of deformation.