Mathematics - Florida State University

 Hall Colloquium



Speaker: Philip Hall.
Title: Large Amplitude Vortex Structures.
Affiliation: Imperial College, University of London.
Date: Friday, September 8, 2000.
Place and Time: Room 101 - Love Building, 3:35-4:35 pm.
Refreshments: Room 204 - Love Building, 3:00 pm.

Abstract. Streamwise vortices play a fundamental role in both transition to turbulence and indeed in fully turbulent flows. In the absence of curvature streamwise vortices can be produced by interacting small amplitude waves whilst in curved flows they can arise in the form of a centrifugal instability. It has been known for some that the control of streamwise vortices is closely linked to the control of turbulent shear flows so that it is vital that the different large amplitude states of the vortices should be understood theoretically.
      In the first part of the seminar we will describe the different mechanisms which produce streamwise vortices. Following the experimental approach of Blackwelder and colleagues we will then focus on centrifugally induced vortices and discuss theoretically the range of nonlinear states which they can assume. The analysis shows that weakly nonlinear theories are somewhat irrelevant to vortex flows but that remarkably we can find closed form solutions of vortex flows which are in fact so large that they completely restructure the flow in which they develop. In the viscous case we derive by a formal expansion procedure a solvability condition on the vortex in the form of a pde to determine the mean flow. Similarly the solvability condition for the mean state produces a pde to determine the vortex so that the flow has similarities with the so-called 'marginal theory of turbulence' suggested many years ago by Malkus. In the inviscid limit we derive new pde evolution equations for 3D unsteady vortices. The theoretical results are related to experimental observations.


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Last modified: Friday September 1st, 2000