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 In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius o ...

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 A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...

called Görtler number (G). It is the ratio of centrifugal effects to the viscous effects in the boundary layer and is defined as :

\mathrm = \frac \left( \frac \right)^

where :

U_e

= external velocity :

\theta

= momentum thickness :

\nu

kinematic viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the int ...

R

= radius of curvature of the wall Görtler instability occurs when G exceeds about 0.3.

Other instances

A similar phenomenon arising from the same centrifugal action is sometimes observed in rotational flows which do not follow a curved wall, such as the rib vortices seen in the wakes of cylinders and generated behind moving structures.

References

* * {{DEFAULTSORT:Gortler Vortices Boundary layers Dimensionless numbers of fluid mechanics Fluid dynamics Fluid dynamic instabilities