In fluid dynamics, helicity is, under appropriate conditions, an invariant of the Euler equations of fluid flow, having a topological interpretation as a measure of linkage and/or knottedness of vortex lines in the flow.
between pressure p and density ρ; and (iii) any body forces acting on the fluid are conservative.
Under these conditions, any closed surface S whose normal vectors are orthogonal to the vorticity (that is,
Then the helicity in V, denoted H, is defined by the volume integral For a localised vorticity distribution in an unbounded fluid, V can be taken to be the whole space, and H is then the total helicity of the flow.
H is invariant precisely because the vortex lines are frozen in the flow and their linkage and/or knottedness is therefore conserved, as recognized by Lord Kelvin (1868).
Helicity is a pseudo-scalar quantity: it changes sign under change from a right-handed to a left-handed frame of reference; it can be considered as a measure of the handedness (or chirality) of the flow.
For two linked unknotted vortex tubes having circulations
, where n is the Gauss linking number of the two tubes, and the plus or minus is chosen according as the linkage is right- or left-handed.
For a single knotted vortex tube with circulation
The invariance of helicity provides an essential cornerstone of the subject topological fluid dynamics and magnetohydrodynamics, which is concerned with global properties of flows and their topological characteristics.
In meteorology,[2] helicity corresponds to the transfer of vorticity from the environment to an air parcel in convective motion.
are perpendicular, making their scalar product nil.
This helicity used in meteorology has energy units per units of mass [m2/s2] and thus is interpreted as a measure of energy transfer by the wind shear with altitude, including directional.
This notion is used to predict the possibility of tornadic development in a thundercloud.
In this case, the vertical integration will be limited below cloud tops (generally 3 km or 10,000 feet) and the horizontal wind will be calculated to wind relative to the storm in subtracting its motion: where
Critical values of SRH (Storm Relative Helicity) for tornadic development, as researched in North America,[3] are: Helicity in itself is not the only component of severe thunderstorms, and these values are to be taken with caution.
[4] That is why the Energy Helicity Index (EHI) has been created.
It is the result of SRH multiplied by the CAPE (Convective Available Potential Energy) and then divided by a threshold CAPE: This incorporates not only the helicity but the energy of the air parcel and thus tries to eliminate weak potential for thunderstorms even in strong SRH regions.