It is well known that the Navier-Stokes equations of viscous fluid flow do not give good predictions of when a viscous flow is likely to become unstable. When classical linearized theory is used to explore the stability of a viscous flow, the Navier-Stokes equations predict that instability will occur at fluid speeds (Reynolds numbers) far in excess of those actually measured in experiments. In response to this discrepancy, theories have arisen that suggest the eigenvalues computed in classical stability analysis do not give a full account of the behaviour, while others have suggested that fluid instability is a fundamentally non-linear process which is not accessible to linearized stability analyses.
In this talk, an alternative account of fluid instability and turbulence will be explored. It is suggested that the Navier-Stokes equations themselves might not be entirely appropriate to describe the transition to turbulent flow. A slightly more general model allows the possibility that the classical viscous fluid flows predicted by Navier-Stokes theory may become unstable at Reynolds numbers much closer to those seen in experiments, and so might perhaps give an account of the physics underlying turbulent behaviour.
- Industrial and Applied Mathematics Seminar