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CATEGORIES:Fluid Mechanics (DAMTP)
SUMMARY:Computing steady vortex flows of prescribed topolo
gy - Paulo Luzzatto-Fegiz (Damtp)
DTSTART;TZID=Europe/London:20130222T160000
DTEND;TZID=Europe/London:20130222T170000
UID:TALK42525AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/42525
DESCRIPTION:Problems involving the evolution of coherent fluid
structures arise within a wide range of situation
s\, including planetary flows (Carton\, 2001)\, fl
uid turbulence (Dritschel et al.\, 2008)\, aquatic
animal propulsion (Dabiri\, 2009)\, and wind turb
ine wakes (SÃ¸rensen 2011). Steady solutions can pl
ay a special role in characterizing the dynamics:
stable flows might be realized in practice\, while
unstable ones may act as attractors in the unstea
dy evolution of the flow. \n\nIn this talk\, we co
nsider the problem of finding steady states of the
two-dimensional Euler equation from topology-pres
erving rearrangements of a given vorticity distrib
ution. We begin by briefly reviewing a range of av
ailable numerical methodologies. We then focus on
a recently introduced technique\, which enables th
e computation of steady vortices with (1) compact
vorticity support\, (2) prescribed topology\, (3)
multiple scales\, (4) arbitrary stability\, and (5
) arbitrary symmetry. We illustrate this methodolo
gy by computing several families of vortex equilib
ria. To the best of our knowledge\, the present wo
rk is the first to resolve nonsingular\, asymmetri
c steady vortices in an unbounded flow. In additio
n\, we discover that\, as a limiting solution is a
pproached\, each equilibrium family traces a clock
wise spiral in a velocity-impulse diagram\; each t
urn of this spiral is also associated with a loss
of stability. Such spiral structure is suggested t
o be a universal feature of steady\, uniform-vorti
city Euler flows. Finally\, we examine the problem
of selecting vorticity distributions that accurat
ely model practically important flows\, and build
a constructive procedure to compute attractors of
the Navier-Stokes equations. We consider an exampl
e involving a vortex pair with distributed vortici
ty\, and obtain good agreement with data from Dire
ct Numerical Simulations.
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberfor
ce Road\, Cambridge
CONTACT:Dr Ed Brambley
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