Part III. the dispersion, under gravity, of a column of fluid supported on a rigid horizontal plane

Abstract

The dispersive motion of a fluid column, collapsing under its own weight whilst immersed in a lighter fluid, both fluids resting on a rigid horizontal bottom, is idealized as a symmetric problem of incompressible potential flow. The velocity potentials in the two fluids are functions of two space-variables and time, and satisfy Laplace’s equation in the two space-variables; and the principal boundary conditions are that, at every point of the fluid interface, the two fluid pressures are equal, and the two normal fluid velocities are both equal to the normal velocity of the interface itself. The initial accelerations of the boundary of a column of semicircular cross-section are derived analytically. An approximate numerical method of solution for the early stages of such a motion is obtained by satisfying these boundary conditions at only a finite number of angular positions instead of everywhere on the fluid interface. Some calculations by this method are shown for certain fluid columns in vacuo . Alternatively, by neglecting vertical accelerations in the motion, the problem is reduced to one of hyperbolic type in one space-variable and time, and this approximation may be solved by the numerical method of characteristics. Some calculations of this type are also shown, in which vertical accelerations have been neglected ab initio , and which are therefore appropriate to initially squat columns. The hydrodynamical problem of the collapse of a fluid column surrounded by a second lighter fluid, both resting on a rigid horizontal plane, was suggested by the ‘base surge’ observed at the Atomic Weapon Trials at Bikini.