Görtler vortices

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

$\mathrm{G} = \frac{U_e \theta}{\nu} \left( \frac{\theta}{R} \right)^{1/2}$

where

$U_e$ = external velocity

$\theta$ = momentum thickness

$\nu$ = kinematic viscosity

$R$ = radius of curvature of the wall

Görtler instability occurs when G exceeds, about 0.3.

References

• Görtler, H. (1955). "Dreidimensionales zur Stabilitätstheorie laminarer Grenzschichten". Journal of Applied Mathematics and Mechanics 35 (9–10): 362–363. doi:10.1002/zamm.19550350906.
• Saric, W. S. (1994). "Görtler vortices". Annu. Rev. Fluid Mech. 26: 379–409. Bibcode:1994AnRFM..26..379S. doi:10.1146/annurev.fl.26.010194.002115.