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SUMMARY:Computing steady vortex flows of prescribed topology - Paulo Luzza
 tto-Fegiz (Damtp)
DTSTART:20130222T160000Z
DTEND:20130222T170000Z
UID:TALK42525@talks.cam.ac.uk
CONTACT:Dr Ed Brambley
DESCRIPTION:Problems involving the evolution of coherent fluid structures 
 arise within a wide range of situations\, including planetary flows (Carto
 n\, 2001)\, fluid turbulence (Dritschel et al.\, 2008)\, aquatic animal pr
 opulsion (Dabiri\, 2009)\, and wind turbine wakes (Sørensen 2011). Steady
  solutions can play a special role in characterizing the dynamics: stable 
 flows might be realized in practice\, while unstable ones may act as attra
 ctors in the unsteady evolution of the flow. \n\nIn this talk\, we conside
 r the problem of finding steady states of the two-dimensional Euler equati
 on from topology-preserving rearrangements of a given vorticity distributi
 on. We begin by briefly reviewing a range of available numerical methodolo
 gies. We then focus on a recently introduced technique\, which enables the
  computation of steady vortices with (1) compact vorticity support\, (2) p
 rescribed topology\, (3) multiple scales\, (4) arbitrary stability\, and (
 5) arbitrary symmetry. We illustrate this methodology by computing several
  families of vortex equilibria. To the best of our knowledge\, the present
  work is the first to resolve nonsingular\, asymmetric steady vortices in 
 an unbounded flow. In addition\, we discover that\, as a limiting solution
  is approached\, each equilibrium family traces a clockwise spiral in a ve
 locity-impulse diagram\; each turn of this spiral is also associated with 
 a loss of stability. Such spiral structure is suggested to be a universal 
 feature of steady\, uniform-vorticity Euler flows. Finally\, we examine th
 e problem of selecting vorticity distributions that accurately model pract
 ically important flows\, and build a constructive procedure to compute att
 ractors of the Navier-Stokes equations. We consider an example involving a
  vortex pair with distributed vorticity\, and obtain good agreement with d
 ata from Direct Numerical Simulations. 
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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