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In [[fluid dynamics]], '''Görtler vortices''' are secondary flows that appear in a [[boundary layer flow]] along a concave wall. If the boundary layer is thin compared to the [[Radius of curvature (mathematics)|radius of curvature]] of the wall, the pressure remains constant across the boundary layer. On the other hand, if the boundary layer thickness is comparable to the radius of curvature, the centrifugal action creates a pressure variation across the boundary layer. This leads to the centrifugal instability (Görtler instability) of the boundary layer and consequent formation of Görtler vortices.
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==Görtler number==
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The onset of Görtler vortices can be predicted using the [[dimensionless number]] called '''Görtler number''' ('''G'''). It is the ratio of centrifugal effects to the viscous effects in the boundary layer and is defined as
:<math>
\mathrm{G} = \frac{U_e \theta}{\nu} \left( \frac{\theta}{R} \right)^{1/2}
</math>
where
: <math>U_e</math> = external velocity
: <math>\theta</math> = [[momentum thickness]]
: <math>\nu</math> = [[Viscosity#Kinematic viscosity|kinematic viscosity]]
: <math>R</math> = radius of curvature of the wall
 
Görtler instability occurs when G exceeds, about 0.3.
 
==References==
*{{cite journal |last=Görtler |first=H. |title={{lang|de|Dreidimensionales zur Stabilitätstheorie laminarer Grenzschichten}} |journal=[[Journal of Applied Mathematics and Mechanics]] |volume=35 |issue=9–10 |pages=362–363 |year=1955 |doi=10.1002/zamm.19550350906 }}
*{{cite journal |last=Saric |first=W. S. |title=Görtler vortices |journal=[[Annual Review of Fluid Mechanics|Annu. Rev. Fluid Mech.]] |volume=26 |issue= |pages=379–409 |year=1994 |doi=10.1146/annurev.fl.26.010194.002115 |bibcode = 1994AnRFM..26..379S }}
 
{{NonDimFluMech}}
 
{{DEFAULTSORT:Gortler Vortices}}
[[Category:Boundary layers]]
[[Category:Dimensionless numbers of fluid mechanics]]
[[Category:Fluid dynamics]]

Latest revision as of 18:58, 3 July 2014

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