Vortex Kinetic Energy Research Articles

Vortex scattering in two dimensions

The two-dimensional interactions of vortices arising in the abelian Higgs and global U(1) models are studied numerically. We demonstrate the right-angle scattering of two vortices in a head-on collisions for a wide variety of parameters. This confirms the low-energy analytic prediction by Ruback for the critical coupling λ=1 in the abelian Higgs model. The dependence of scattering on impact parameter and initial velocity is also investigated and shown to be relatively velocity independent up to v≈0.4 c. Above this threshold higher mode excitations become important in collisions and the loss of vortex kinetic energy through radiation becomes significant. The metric on the moduli space M 2 of two λ=1 vortex solutions is approximately reconstructed using geodesics from low-velocity collisions. Geometrical properties of the metric and their correspondence to the scattering behaviour are discussed, and the embedding in R 3 is exhibited.

Vortex generation by oscillatory flow over rippled surfaces

Vortices generated by oscillatory flow over symmetrical sand ripples have been investigated in order to ascertain the amount of wave energy loss that can be attributed to the formation and movement of vortices. The experimental phase of the investigation centered around the flow visualization of the vortices over the ripples. These laboratory data were used to obtain values for three parameters (vortex size, ciculation, and radius of the vortex core) needed to evaluate the amount of energy bound up in the vortex, the energy relationship being derived from a trapped vortex model. Comparison of the vortex kinetic energy loss attributed to bottom effects indicates that the vortices possess about 7% of the measured wave energy loss, the majority of the remaining energy loss being attributed to bottom shear.

Threshold conditions for vortex-stabilized electrical discharges in the atmosphere

Laboratory experiments with vortex-stabilized arcs show that any effect the vortex may have in decreasing the deionization rate between pulses of power to the arc was too small to be measured with available apparatus. The major function of the vortex is to keep the plasma in contact with the electrodes, and a secondary function is to hold the plasma column on the shortest spacing between the electrodes. The concentration of the plasma by centrifugal action of the vortex gives only a 13% reduction in arc threshold power at the expense of a threefold increase in vortex kinetic energy. This effect is less important than previous experiments have indicated. The threshold power density of the arc is essentially a constant at 52 watts/cm3 and does not change appreciably over a threefold change in vortex kinetic energy. Tests with hard sparks did not show any preference for the axis of the vortex, but sparks occurring in rapid succession, say 10 to 20 per second, tend to restrike in the same channel more often in the vortex than elsewhere. Multistroke cloud-to-ground lightning discharges may not show preference for a tornado axis, since, owing to the absence of electrodes, the vortex will not play the same role as in the laboratory experiments.