On the stability of the Jeffery–Hamel flow

Abstract

The Jeffery–Hamel flow is analyzed by making use of a mechanical analogy. The solutions are generated by a finite element method, for the corresponding least action principle and are valid for any width of the channel. Then, the Galerkin method is used to study the linear and temporal stability of some flows for small widths of the channel. An argument is given to show that pure inflow should be unstable for small widths of the channel, a result which is corroborated by our numerical calculations. We find that the flows IOI and IO are unstable for Reynolds numbers near zero. A stability window for some asymmetric flows and certain widths is also found.