MATHEMATICS 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, 3:354:35 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 socalled '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.
