- Helicity (fluid mechanics)
:"this page is about helicity in fluid mechanics. For helicity of magnetic fields, see

magnetic helicity . For helicity inparticle physics , seehelicity (particle physics) ."In

fluid mechanics ,**helicity**is the extent to whichcorkscrew -like motion occurs. If a parcel of fluid is moving, undergoingsolid body motion rotating about an axis parallel to the direction of motion, it will have helicity. If the rotation isclockwise when viewed from ahead of the body, the helicity will be positive, if counterclockwise, it will be negative.Formally, helicity is defined as

:$H=intmathbf\{u\}cdotleft(\; abla\; imesmathbf\{u\}\; ight),d^3\{mathbf\; r\}.$

The concept is interesting because it is a conserved quantity: $H$ 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 .**Meteorology**In

meteorology [*cite web|url=http://homepage.ntlworld.com/booty.weather/FAQ/2A.htm#2A.24|title=Definitions of terms in meteorology|author="Martin Rowley" retired*] , helicity correspond to the transfer ofmeteorologist withUKMET |accessdate=2006-07-15vorticity from the environment to an air parcel in convective motion. Here the definition of helicity is simplified to only use the horizontal component ofwind andvorticity :::$H\; =\; int\{\; vec\; V\_h\}\; cdot\; vec\; zeta\_h\; ,d\{mathbf\; Z\}\; =\; int\{\; vec\; V\_h\}\; cdot\; abla\; imes\; V\_h\; ,d\{mathbf\; Z\}qquad\; qquad\; egin\{cases\}\; Z\; =\; Altitude\; \backslash \; V\_h\; =\; Horizontal\; velocity\; \backslash \; zeta\_h\; =\; Horizontal\; vorticity\; end\{cases\}$

According to this formula, if the horizontal wind does not change direction with

altitude , H will be zero as the product of $V\_h$ and $abla\; imes\; V\_h$ areperpendicular one to the other making theirscalar product nil. H is then positive if the wind turns (clockwise ) with altitude and negative if it backs (counter-clockwise ). Helicity has energy units per units of mass ($\{m^2\}/\{s^2\}$) 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 belowcloud tops (generally 3 km or 10,000 feet) and the horizontal wind will be calculated to wind relative to thestorm in subtracting its motion:::$SRH\; =\; int\{\; left\; (\; vec\; V\_h\; -\; C\; ight\; )\}\; cdot\; abla\; imes\; V\_h\; ,d\{mathbf\; Z\}qquad\; qquad\; egin\{cases\}\; C\; =\; Cloud\; motion\; to\; the\; ground\; end\{cases\}$

Critical values of SRH (

**S**torm**R**elative**H**elicity) for tornadic development, as researched inNorth America [*cite web|url=http://www.spc.noaa.gov/exper/mesoanalysis/s6/index2.html |title=*] , are:**EXPLANATION OF SPC SEVERE WEATHER PARAMETERS**|author=Storm Prediction Center |publisher=National Weather Service |accessdate=2006-07-15* SRH = 150-299 ...

supercell s possible with weaktornadoes according toFujita scale

* 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

thunderstorm 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 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. The critical values of EHI:* EHI = 1 ... possible tornadoes

* EHI = 1-2 ... moderate to strong tornadoes

* EHI > 2 ... strong tornadoes**References****Bibliography*** Batchelor, G.K., (1967, reprinted 2000) "An Introduction to Fluid Dynamics", Cambridge Univ. Press

* Ohkitani, K., "Elementary Account Of Vorticity And Related Equations". Cambridge University Press. January 30, 2005. ISBN 0-521-81984-9

* Chorin, Alexandre J., "Vorticity and Turbulence". Applied Mathematical Sciences, Vol 103, Springer-Verlag. March 1, 1994. ISBN 0-387-94197-5

* Majda, Andrew J., Andrea L. Bertozzi, "Vorticity and Incompressible Flow". Cambridge University Press; 1st edition. December 15, 2001. ISBN 0-521-63948-4

* Tritton, D. J., "Physical Fluid Dynamics". Van Nostrand Reinhold, New York. 1977. ISBN 0-19-854493-6

* Arfken, G., "Mathematical Methods for Physicists", 3rd ed. Academic Press, Orlando, FL. 1985. ISBN 0-12-059820-5

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