The rise and distortion of a two-dimensional gas bubble in an inviscid liquid

A two-dimensional gas bubble moves under gravity in an inviscid incompressible liquid. Boundary-integral methods are used to calculate the shape and position of the bubble surface. Two independent codes, based on the point-vortex method and the surface-dipole method, give results in good agreement with each other, up to the time of incipient self-intersection of the bubble surface. The results agree with previous theoretical work, valid over a smaller time interval of Baumel et al. [Can. J. Phys. 60, 999 (1982)] but there are quantitative differences with the experimental work of Walters and Davidson [J. Fluid Mech. 12, 408 (1962)]. The jet that forms at the rear of the bubble is taller and thinner in the calculations than in the experiments. Surface tension effects reduce the discrepancy only slightly. The evolution of the bubble surface is shown to be very sensitive to initial perturbations of bubble shape. If these have high enough wavenumber, Rayleigh–Taylor jets form on the upper surface.