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SUMMARY:On the large-scale structure of two-dimensional turbulence - David
 son\, PA (Cambridge)
DTSTART:20081001T080000Z
DTEND:20081001T083000Z
UID:TALK13846@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We consider freely-decaying\, two-dimensional\, isotropic turb
 ulence. It is usually assumed that\, in such turbulence\, the energy spect
 rum at small wavenumber\, k\, takes the form E(k->0)=Ik^3 \, where I is th
 e two-dimensional version of Loitsyanskys integral. However\, a second pos
 sibility is E(k->0)=Lk \, where the pre-factor\, L\, is the two-dimensiona
 l analogue of Saffmans integral. We show that\, as in three dimensions\, L
  is an invariant and that E~Lk spectra arise whenever the eddies possess a
  significant amount of linear impulse. The conservation of L is shown to b
 e a direct consequence of the principle of conservation of linear momentum
 . We also show that isotropic turbulence dominated by a cloud of randomly 
 located monopole vortices has a singular energy spectrum of the form E(k->
 0)=Jk^-1\, where J\, like L\, is an invariant. However\, while E~Jk^-1 nec
 essarily implies the existence of a sea of monopoles\, the converse need n
 ot be true: a sea of monopoles whose spatial locations are not entirely ra
 ndom\, but constrained in some way\, need not give a E~Jk^-1 spectra. The 
 constraint imposed by the conservation of energy is particularly important
 \,ruling out E~Jk^-1 spectra for certain classes of initial conditions.\n\
 nWe illustrate these ideas with some direct numerical simulations. 
LOCATION:Seminar Room 1\, Newton Institute
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