Stability of viscous flow over concave cylindrical surfaces

Abstract

The stability for three-dimensional disturbances of viscous flow over concave cylindrical surfaces is investigated by the method of asymptotic solutions. The results confirm Görtler’s conclusions that these disturbances can only take place on concave surfaces, and that in the critical condition that the parameter R δ (δ/ r ) ½ remains constant, where R δ is Reynolds number and δ/r is the ratio of the thickness of the boundary layer to the radius of curvature. Additionally, it is found that there are many steady states, and the values R δ (δ/ r ) ½ are evaluated for the first two states. For a fixed Rδ(δ / r ) ½ there is a finite number of steady states.