The Effect of Symmetry on the Hydrodynamic Stability of and Bifurcation from Planar Shear Flows
Abstract
A new approach to boundary layer transition has been developed based on the use of dynamical systems theory in a spatial setting. The results extend the classic theory of spatial stability into the nonlinear regime and a theory for spatial Hopf bifurcation, spatial Floquet theory, wavelength doubling and spatially quasi-periodic states has been developed and applied to the boundary layer problem. The demonstration of the prevalence of spatially quasi-periodic states (in the Blasius boundary layer) is important for applications because it provides the first mathematically consistent theory for the appearance of spatially quasi-periodic states in shear flows which have been observed in experiments. Exact symmetries in the Navier-Stokes equations and normal form symmetries play a basic role in the theory and require use of equivariant dynamical systems theory. Scenarios for the transition to turbulence are easily postulated in the spatial (convective) framework and a conjecture on the transition to 'convective' turbulence through wavelength doubling is introduced.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1990
- Accession Number
- ADA232916
Entities
People
- Thomas J. Bridges
Organizations
- Worcester Polytechnic Institute