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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==
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]]

Revision as of 15:30, 7 February 2013

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 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.

Görtler number

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

G=Ueθν(θR)1/2

where

Ue = external velocity
θ = momentum thickness
ν = kinematic viscosity
R = radius of curvature of the wall

Görtler instability occurs when G exceeds, about 0.3.

References

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