Accession Number:

ADA232916

Title:

The Effect of Symmetry on the Hydrodynamic Stability of and Bifurcation from Planar Shear Flows

Descriptive Note:

Final rept. 1 Sep 1988-31 Dec 1989

Corporate Author:

WORCESTER POLYTECHNIC INST MA

Personal Author(s):

• Bridges, Thomas J.

Report Date:

1990-12-01

Pagination or Media Count:

71.0

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.

Descriptors:

• *BOUNDARY LAYER TRANSITION
• *SHEAR FLOW
• SPATIAL DISTRIBUTION
• STABILITY
• DYNAMICS
• THEORY
• CONVECTION
• TURBULENCE
• CONSISTENCY
• NONLINEAR SYSTEMS
• BOUNDARY VALUE PROBLEMS
• PLANAR STRUCTURES
• TRANSITIONS
• FLOW
• NAVIER STOKES EQUATIONS
• BIFURCATION(MATHEMATICS)
• HYDRODYNAMICS
• PERIODIC FUNCTIONS
• SETTING(ADJUSTING)
• SHEAR PROPERTIES
• MATHEMATICAL MODELS

Subject Categories:

• Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE