Impulse of a Vortex System in a Bounded Fluid
We derive, from the equation of motion of a classical constant-density fluid, the dynamic equation for the fluid impulse of a vortex system in a bounded charged or uncharged fluid. The result is an integral theorem which primarily describes the effect of nonpotential forces upon the vorticity ω ≡ ∇ × v [or ω ≡∇ × v + (q/m) B field for charged fluids]. Although the equations treat ω as a continuous field, the main application of the theorem* has been to quantum fluids where a vortex core is usually considered to be a δ-function singularity in the field ∇ × v. Figure 1, however, shows how the concept of a continuous vorticity field can be applied to a quantum fluid if we redefine w as the curl of the physical current j = ρv.
KeywordsGauge Transformation Vortex Ring Vortex Core Vorticity Field Potential Force
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