Editing Hydrodynamical helicity (section)

==Meteorology==
In [[meteorology]],<ref>{{cite web|url=http://homepage.ntlworld.com/booty.weather/FAQ/2A.htm#2A.24 |title=Definitions of terms in meteorology |author=''Martin Rowley'' retired [[meteorologist]] with [[UKMET]] |access-date=2006-07-15 |archive-url=https://web.archive.org/web/20060516011557/http://homepage.ntlworld.com/booty.weather/FAQ/2A.htm#2A.24 |archive-date=2006-05-16 |url-status=dead }}</ref> helicity corresponds to the transfer of [[vorticity]] from the environment to an air parcel in [[convection|convective]] motion. Here the definition of helicity is simplified to only use the horizontal component of [[wind]] and [[vorticity]], and to only integrate in the vertical direction, replacing the volume integral with a one-dimensional [[definite integral]] or [[line integral]]:

:<math>
H = \int_{Z_1}^{Z_2}{ \vec V_h} \cdot \vec \zeta_h \,d{Z} = \int_{Z_1}^{Z_2}{ \vec V_h} \cdot \nabla \times \vec V_h  \,d{Z} ,</math>

where
*{{tmath|Z}} is the altitude,
*{{tmath|\vec V_h}} is the horizontal velocity,
*{{tmath|\vec \zeta_h}} is the horizontal vorticity.

According to this formula, if the horizontal wind does not change direction with [[altitude]], {{mvar|H}} will be zero as <math>V_h</math> and <math>\nabla \times V_h</math> are [[perpendicular]], making their [[scalar product]] nil. {{mvar|H}} is then positive if the wind veers (turns [[clockwise]]) with altitude and negative if it backs (turns [[counterclockwise]]). This helicity used in meteorology has energy units per units of mass [m{{sup|2}}/s{{sup|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 [[tornado|tornadic]] development in a [[thundercloud]]. In this case, the vertical integration will be limited below [[cloud]] tops (generally 3&nbsp;km or 10,000 feet) and the horizontal wind will be calculated to wind relative to the [[storm]] in subtracting its motion:

::<math>\mathrm{SRH} = \int_{Z_1}^{Z_2}{ \left ( \vec V_h - \vec C \right )}  \cdot \nabla \times \vec V_h  \,d{Z} </math>
where {{tmath|\vec C}} is the cloud motion relative to the ground.

Critical values of SRH ('''S'''torm '''R'''elative '''H'''elicity) for tornadic development, as researched in [[North America]],<ref>{{cite web |author=Thompson |first=Rich |author-link= |title=Explanation of SPC Severe Weather Parameters |url=https://www.spc.noaa.gov/exper/mesoanalysis/help/begin.html |url-status=live |archive-url=https://web.archive.org/web/20221229175208/https://www.spc.noaa.gov/exper/mesoanalysis/help/begin.html |archive-date=December 29, 2022 |access-date=February 13, 2023 |website=[[National Weather Service]] - [[Storm Prediction Center]] |publisher=[[NOAA]]}}</ref> are:

* SRH = 150-299 ... [[supercell]]s possible with weak [[tornadoes]] according to [[Fujita scale]]
* SRH = 300-499 ... very favourable to supercells development and strong tornadoes
* SRH > 450 ... violent tornadoes
* When calculated only below 1&nbsp;km (4,000 feet), the cut-off value is 100.

Helicity in itself is not the only component of severe [[thunderstorm]]s, and these values are to be taken with caution.<ref>{{cite web|title=Storm Relative Helicity|url=http://www.spc.noaa.gov/exper/mesoanalysis/help/help_srh.html|publisher=NOAA|access-date=8 August 2014}}</ref> 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:

:<math>\mathrm{EHI} = \frac{\mathrm{CAPE} \times \mathrm{SRH}}{\text{160,000}}</math>

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