Helicity (fluid mechanics)
Encyclopedia
In fluid mechanics
, helicity is the extent to which helix
-like motion occurs. If a parcel of fluid is moving, undergoing solid body motion rotating about an axis parallel to the direction of motion, it will have helicity. If the rotation is clockwise
when viewed from ahead of the body, the helicity will be positive, if counterclockwise, it will be negative.
Formally, helicity is defined as
The concept is interesting because it is a conserved quantity
:
is unchanged in a fluid obeying the Euler equations
(i.e. zero viscosity) for incompressible fluids
.
This is analogous to the conservation of magnetic helicity
.
Helicity is a useful concept in theoretical descriptions of turbulence
.
, helicity corresponds to the transfer of vorticity from the environment to an air parcel in convective
motion. Here the definition of helicity is simplified to only use the horizontal component of wind
and vorticity:
Fluid mechanics
Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...
, helicity is the extent to which helix
Helix
A helix is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helixes are coil springs and the handrails of spiral staircases. A "filled-in" helix – for...
-like motion occurs. If a parcel of fluid is moving, undergoing solid body motion rotating about an axis parallel to the direction of motion, it will have helicity. If the rotation is clockwise
Clockwise
Circular motion can occur in two possible directions. A clockwise motion is one that proceeds in the same direction as a clock's hands: from the top to the right, then down and then to the left, and back to the top...
when viewed from ahead of the body, the helicity will be positive, if counterclockwise, it will be negative.
Formally, helicity is defined as
The concept is interesting because it is a conserved quantity
Conservation law
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....
:
is unchanged in a fluid obeying the Euler equationsEuler equations
In fluid dynamics, the Euler equations are a set of equations governing inviscid flow. They are named after Leonhard Euler. The equations represent conservation of mass , momentum, and energy, corresponding to the Navier–Stokes equations with zero viscosity and heat conduction terms. Historically,...
(i.e. zero viscosity) for incompressible fluids
Incompressible flow
In fluid mechanics or more generally continuum mechanics, incompressible flow refers to flow in which the material density is constant within an infinitesimal volume that moves with the velocity of the fluid...
.
This is analogous to the conservation of magnetic helicity
Magnetic helicity
In plasma physics, magnetic helicity is the extent to which a magnetic field "wraps around itself". It is a generalization of the topological concept of linking number to the differential quantities required to describe the magnetic field...
.
Helicity is a useful concept in theoretical descriptions of turbulence
Turbulence
In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...
.
Meteorology
In meteorologyMeteorology
Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...
, helicity corresponds to the transfer of vorticity from the environment to an air parcel in convective
Convection
Convection is the movement of molecules within fluids and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids....
motion. Here the definition of helicity is simplified to only use the horizontal component of wind
Wind
Wind is the flow of gases on a large scale. On Earth, wind consists of the bulk movement of air. In outer space, solar wind is the movement of gases or charged particles from the sun through space, while planetary wind is the outgassing of light chemical elements from a planet's atmosphere into space...
and vorticity:
-
According to this formula, if the horizontal wind does not change direction with altitudeAltitudeAltitude or height is defined based on the context in which it is used . As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context...
, H will be zero as the product of
and 
are perpendicularPerpendicularIn geometry, two lines or planes are considered perpendicular to each other if they form congruent adjacent angles . The term may be used as a noun or adjective...
one to the other making their scalar product nil. H is then positive if the wind veers (turns clockwiseClockwiseCircular motion can occur in two possible directions. A clockwise motion is one that proceeds in the same direction as a clock's hands: from the top to the right, then down and then to the left, and back to the top...
) with altitude and negative if it backs (turns counter-clockwise). Helicity has energy units per units of mass (
) 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 tornadicTornadoA tornado is a violent, dangerous, rotating column of air that is in contact with both the surface of the earth and a cumulonimbus cloud or, in rare cases, the base of a cumulus cloud. They are often referred to as a twister or a cyclone, although the word cyclone is used in meteorology in a wider...
development in a thundercloud. In this case, the vertical integration will be limited below cloudCloudA cloud is a visible mass of liquid droplets or frozen crystals made of water and/or various chemicals suspended in the atmosphere above the surface of a planetary body. They are also known as aerosols. Clouds in Earth's atmosphere are studied in the cloud physics branch of meteorology...
tops (generally 3 km or 10,000 feet) and the horizontal wind will be calculated to wind relative to the stormStormA storm is any disturbed state of an astronomical body's atmosphere, especially affecting its surface, and strongly implying severe weather...
in subtracting its motion:
-
Critical values of SRH (Storm Relative Helicity) for tornadic development, as researched in North AmericaNorth AmericaNorth America is a continent wholly within the Northern Hemisphere and almost wholly within the Western Hemisphere. It is also considered a northern subcontinent of the Americas...
, are:
- SRH = 150-299 ... supercellSupercellA supercell is a thunderstorm that is characterized by the presence of a mesocyclone: a deep, continuously-rotating updraft. For this reason, these storms are sometimes referred to as rotating thunderstorms...
s possible with weak tornadoes according to Fujita scaleFujita scaleThe Fujita scale , or Fujita-Pearson scale, is a scale for rating tornado intensity, based primarily on the damage tornadoes inflict on human-built structures and vegetation... - SRH = 300-499 ... very favourable to supercells development and strong tornadoes
- SRH > 450 ... violent tornadoes
- When calculated only below 1 km (4,000 feet), the cut-off value is 100.
Helicity in itself is not the only component of severe thunderstormThunderstormA thunderstorm, also known as an electrical storm, a lightning storm, thundershower or simply a storm is a form of weather characterized by the presence of lightning and its acoustic effect on the Earth's atmosphere known as thunder. The meteorologically assigned cloud type associated with the...
s and those values are to be taken with caution. That is why the Energy Helicity Index (EHI) has been created. It is the result of SRH multiplied by the CAPE (Convective Available Potential EnergyConvective available potential energyIn meteorology, convective available potential energy , sometimes, simply, available potential energy , is the amount of energy a parcel of air would have if lifted a certain distance vertically through the atmosphere...
) and then divided by a threshold CAPE: EHI = (CAPE x SRH) / 160,000. 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. The critical values of EHI:
- EHI = 1 ... possible tornadoes
- EHI = 1-2 ... moderate to strong tornadoes
- EHI > 2 ... strong tornadoes
- SRH = 150-299 ... supercell
-