Where does helicity collide?

In particle physics, helicity is the sign of a particle's spin projected onto its direction of motion: right-handed when spin and momentum point the same way, left-handed when they oppose. Goldhaber, Grodzins, and Sunyar's 1958 Helicity of neutrinos measured this for the neutrino and found it left-handed, a landmark for the weak interaction and parity violation. The referent is a two-valued (±) chirality property of a moving quantum particle, and it is unrelated to the flow-topology quantity fluid dynamicists call helicity beyond the shared intuition of handedness.[1]

Unit

The sign (±) of spin projected onto momentum

Recovery means

Not applicable

Measured by

Inferred from decay and scattering experiments that resolve spin orientation relative to particle momentum

In fluid dynamics, helicity is the volume integral of the dot product of the velocity and vorticity fields, a measure of how much a flow's vortex lines are twisted and linked. Moffatt's 1969 The degree of knottedness of tangled vortex lines showed that this quantity is a topological invariant of an ideal fluid, fixed by the linkage of its vortex tubes. The referent is a global property of a flow field describing its handedness and the knottedness of its vorticity, conserved in inviscid flow, and distinct from a particle's spin sign despite the shared name.[2]

Unit

The integral of velocity·vorticity over the flow volume (m⁴ s⁻²)

Recovery means

Not applicable

Measured by

Computed from measured or simulated velocity and vorticity fields as their integrated inner product

In meteorology, storm-relative helicity applies the same velocity–vorticity integral to the air feeding a thunderstorm, gauging how much of the low-level shear is streamwise so that inflowing air already spins about a horizontal axis the updraft can tilt into rotation. Davies-Jones's 1984 Streamwise vorticity: The origin of updraft rotation in supercell storms established that streamwise vorticity, integrated this way, controls whether an updraft acquires supercell rotation. It is the identical construct as fluid helicity, specialised to the storm-inflow layer and used operationally as a severe-weather and tornado forecast parameter.[3]

Unit

Storm-relative helicity over an inflow depth (m² s⁻²)

Recovery means

Not applicable

Measured by

Integrated from the vertical wind profile as the storm-relative winds cross the horizontal vorticity, typically over the lowest 1–3 km