FRONT SPEEDS FOR AXISYMMETRIC
GRAVITY CURRENTS

P. J. MONTGOMERY AND T. B. MOODIE

Abstract. The initial phase of gravity current slumping caused by the instantaneous release of a cylinder of dense fluid is considered theoretically and numerically. The resulting axisymmetric flow is examined in the framework of the solution to a system of nonlinear hyperbolic partial differential equations for which the advancing front of the gravity current is considered as a jump discontinuity in the solution. The Rankine-Hugoniot jump conditions are employed to determine the possible front conditions that such a jump may take. In the nonrotating case, the standard Froude number relationship is obtained, while in the rotating case, an approximation for constant rotation is derived. These relationships are tested through numerical solutions of the equations of motion, and the new front condition is shown to be an improvement on the standard one.