Conditional symmetric instability: Difference between revisions

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::* '''If <math>\theta_e</math> diminish with altitude leads to unstable airmass'''

::* '''If <math>\theta_e</math> remains the same with altitude leads to neutral airmass'''

::* '''If <math>\theta_e</math> increase with altitude leads to stable airmass.'''

===Inertial Stability===

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In the same way, a lateral displacement of an air particle changes its absolute vorticity <math>\eta</math>. This is given by the sum of the planetary vorticity, <math>f</math>, and <math>\zeta</math>, the [[Geostrophic wind|geostrophic]] (or relative) vorticity of the parcel:<ref name="Doswell"/><ref name="MF-2">{{cite web|language=French | url= http://www.meteofrance.fr/publications/glossaire?articleId=152385 | title= Instabilité barocline | publisher= [[Météo-France]] | accessdate= August 23, 2019 | work= Glossaire météorologique }}</ref>

<{{center>|<math>\eta= \left[ \frac{\partial v}{\partial x} - \frac{\partial u}{\partial y} \right ] + f = \zeta + f \qquad \qquad </math></center>}}

Where :

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<math>\eta</math> can be positive, null or negative depending on the conditions in which the move is made. As the absolute vortex is almost always positive on the [[synoptic scale]], one can consider that the atmosphere is generally stable for lateral movement. Inertial stability is low only when <math>\eta</math> is close to zero. Since <math>f</math> is always positive, <math>\eta \le 0 </math> can be satisfied only on the anticyclonic side of a strong maximum of [[jet stream]] or in a [[Ridge (meteorology)|barometric ridge]] at altitude, where the derivative velocities in the direction of displacement in the equation give a significant negative value.<ref name="Moore" />

The variation of the [[angular momentum]] indicate the stability:<ref name="Doswell"/><ref name="Moore">{{cite web | language= en | format= ppt | url= http://www.comet.ucar.edu/class/rfc_hydromet/03-1/docs/Moore/Mesoinstab/Meso-proc.ppt | author= James T. Moore | title= Mesoscale Processes | publisher= [[University Corporation for Atmospheric Research|UCAR]] | accessdate= August 23, 2019 | date= 2001 | pages= 10–53 | archive-url= https://web.archive.org/web/20141221040317/http://www.comet.ucar.edu/class/rfc_hydromet/03-1/docs/Moore/Mesoinstab/Meso-proc.ppt | archive-date= December 21, 2014 | url-status= dead }}</ref><ref name=Schultz>{{cite journal | language = en | title= The Use and Misuse of Conditional Symmetric Instability | first1= David M. | last1 = Schultz | first2= Philip N. | last2= Schumacher | journal = [[Monthly Weather Review]] | volume = 127 | issue = 12 | pages = 2709 | date = December 1999 | doi = 10.1175/1520-0493(1999)127<2709:TUAMOC>2.0.CO;2| publisher= [[American Meteorological Society|AMS]] | s2cid= 708227 | issn = 1520-0493| doi-access = free }}</ref>

*<math>\Delta M_g = 0 </math>, the particle then remains at the new position because its momentum has not changed

*<math>\Delta M_g > 0 </math>, the particle returns to its original position because its momentum is greater than that of the environment