The Time-dependent Collapse of a Rotating Fluid Cylinder

Abstract

The behavior of a reduced-gravity cylinder of fluid, released from rest in a rotating system, is considered. The eventual steady state, found by normal principles of conservation of angular momentum, mass, and potential vorticity, is shown to have less energy than the initial state. This energy deficit can be accounted for by time-dependent motions, instabilities, and dissipative effects (waves cannot propagate energy to infinity in this system since the active fluid is of finite extent). We show here that an extra feature, hitherto unconsidered, comes into play. The time-dependent motion allows occasional wave-breaking events, which can act as a mechanism to remove the energy deficit on short (i.e., inertial) time scales. Such a process has not been parameterized in ocean circulation models.