UC Irvine

There are many conditions in which a vortex ring deviates from axisymmetry. The shape of a three dimensional vortex ring represents the axisymmetry of propulsion, which has applications in animal locomotion (e.g., the free-swimming of a jellyfish), rocket and marine propulsion devices as well as blood flow through the heart valves. No fluid dynamics' measure is yet defined to quantify the axisymmetry of a three dimensional vortex ring with a single value. The non-axisymmetry exists, for instance, in the vortex ring formed downstream of the mitral valve of healthy hearts, and helps efficient blood momentum transfer from the left atrium toward the aorta. Here, we introduce an index that measures the deviation of a vortex ring from axisymmetry. This index examines the spectrum of the impulse of a naturally-formed vortex ring and expresses the deviation from axisymmetry in terms of the vortex's impulse. We show that the axisymmetry index is related to the second moment of the vorticity distribution of the ring, i.e., as the second moment of vorticity on one side increases compared to the other side, the axisymmetry index decreases accordingly.