vortex: one construct, many systems

In fluid dynamics a vortex is a region of swirling flow organised around a core line, characterised by its vorticity (the local curl of the velocity) and by the circulation taken around any loop enclosing the core. Helmholtz's 1858 Über Integrale der hydrodynamischen Gleichungen proved the vortex theorems (that in an ideal fluid vortex lines move with the fluid and their strength is conserved), which make the vortex a durable, trackable structure rather than a passing swirl. This is the parent construct: a conserved swirling flow defined by circulation, the same object that reappears quantized in superfluids and as a phase singularity in light.[1]

Unit

The circulation and vorticity organised around a vortex core line

Recovery means

Not applicable

Measured by

Quantified by circulation around a closed loop, the vorticity field, and the core radius

In a superfluid such as liquid helium below the lambda point, the same vortex construct appears but its circulation can take only discrete values set by Planck's constant over the particle mass: a quantized vortex. Feynman's Application of quantum mechanics to liquid helium argued that superfluid rotation is carried entirely by arrays of these quantized vortex lines, each with identical circulation. It is the identical conserved-swirl construct as a classical vortex, now constrained by quantum mechanics so that circulation is parcelled into indivisible units rather than varying continuously.[2]

Unit

Circulation fixed in integer multiples of the quantum h/m around a vortex line

Recovery means

Not applicable

Measured by

Inferred from quantized circulation steps, vortex-lattice imaging, and rotation experiments in superfluids and condensates

In wave optics the vortex construct reappears as an optical vortex: a point or line where the wave amplitude vanishes and the phase winds through a whole number of turns around it, so the wavefront spirals and the beam carries orbital angular momentum. Nye and Berry's Dislocations in wave trains identified these phase singularities as generic features of waves, directly analogous to vortices in a fluid, with circulation replaced by the winding of phase. It is the same topological swirl construct transposed from a moving fluid to a light field, measured by the topological charge of the phase winding rather than by fluid circulation.[3]

Unit

The integer topological charge of the phase winding around a dark core

Recovery means

Not applicable

Measured by

Determined from interferometric phase winding, the topological charge, and orbital-angular-momentum content of the beam