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UID:news2046@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20260526T151509
DTSTART;TZID=Europe/Zurich:20260603T170000
SUMMARY:An Afternoon of Fluid Dynamics: Ali Arslan (ETH Zurich)
DESCRIPTION:We investigate the stability of the magnetohydrodynamic (MHD) e
 quations in the magnetostrophic (inertialess) regime\, a singular limit re
 levant to rapidly rotating planetary cores such as the Earth's. In this re
 gime\, the Navier-Stokes equations reduce to a diagnostic force balance be
 tween the Coriolis force\, buoyancy\, and the Lorentz force. This talk foc
 uses on deriving rigorous necessary conditions for the growth of the magne
 tic energy\, thereby establishing nonlinear "antidynamo" theorems. By empl
 oying an additional poloidal-toroidal decomposition\, we identify regions 
 in parameter space\, defined by the nondimensional Rayleigh\, Reynolds and
  Peclet numbers\, where individual components of magnetic field growth are
  impossible\, corresponding to stability of trivial solutions. A key techn
 ical result is the identification of the L^p norms of temperature gradient
 s and dissipation as critical to the dynamo threshold. The methodology is 
 also applied to the linearised MHD equations\, referred to as the Moffatt-
 Loper equations. Finally\, we discuss the evolution of Ohmic dissipation a
 nd provide necessary conditions corresponding to a new class of nonlinear 
 strong- and weak-field dynamo theory.
X-ALT-DESC:<p>We investigate the stability of the magnetohydrodynamic (MHD)
  equations in the magnetostrophic (inertialess) regime\, a singular limit 
 relevant to rapidly rotating planetary cores such as the Earth's. In this 
 regime\, the Navier-Stokes equations reduce to a diagnostic force balance 
 between the Coriolis force\, buoyancy\, and the Lorentz force. This talk f
 ocuses on deriving rigorous necessary conditions for the growth of the mag
 netic energy\, thereby establishing nonlinear "antidynamo" theorems. By em
 ploying an additional poloidal-toroidal decomposition\, we identify region
 s in parameter space\, defined by the nondimensional Rayleigh\, Reynolds a
 nd Peclet numbers\, where individual components of magnetic field growth a
 re impossible\, corresponding to stability of trivial solutions. A key tec
 hnical result is the identification of the L^p norms of temperature gradie
 nts and dissipation as critical to the dynamo threshold. The methodology i
 s also applied to the linearised MHD equations\, referred to as the Moffat
 t-Loper equations. Finally\, we discuss the evolution of Ohmic dissipation
  and provide necessary conditions corresponding to a new class of nonlinea
 r strong- and weak-field dynamo theory.</p>
DTEND;TZID=Europe/Zurich:20260603T175000
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