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SUMMARY:Some exact nonlinear laminar solutions to the dynamo equations (In
 vited speaker) - Jonathan Mestel (Imperial College London)
DTSTART:20220913T134500Z
DTEND:20220913T143000Z
UID:TALK177491@talks.cam.ac.uk
DESCRIPTION:A few exact solutions to the incompressible\, laminar Navier-S
 tokes and induction equations are examined. To begin with\, velocity field
 s with a simplified structure\, such as similarity flows are derived. Magn
 etic fields with a similar spatial reduction are then sought. If these gro
 w kinematically\, then they can be followed exactly into the nonlinear reg
 ime without approximation. An example is von-Karman flow between two rotat
 ing discs\, a configuration resembling the VKS experiment. The resulting n
 onlinear system reduces to 4 coupled ODEs.\nAlthough some of the "dynamos"
  thus found are axisymmetric\, they are saved from Cowling's theorem by th
 e unbounded domain. It is shown that some of these solutions involve energ
 y being generated locally\, rather than being advected in from infinity.&n
 bsp\;\nThis work involved collaborations with Ali Arslan\, Raquel Vaz\, an
 d Leszek Zabielski
LOCATION:Seminar Room 1\, Newton Institute
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