Görtler vortices

In fluid dynamics, Görtler vortices are secondary flows that appears 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 creats 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. It is the ratio of centrifugal effects to the viscous effects in the boundary layer and is defined as:G = frac{U_e heta}{ u} left( frac{ heta}{R} ight)^{1/2}where: U_e = external velocity: heta = momentum thickness : u = kinematic viscosity: R = radius of curvature of the wall

Görtler instability occurs when G exceeds, about 0.3.

References

*Görtler, H., "Driedimensionales zur stabilitatstheorie laminarer grenzschichten", Z. Agnew. Math. Mech., 35, pp. 362-363 (1955).
*Saric, W. S., "Görtler vortices", Annu. Rev. Fluid Mech., 26, p. 379 (1994).


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