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SUMMARY:Parameterizing interaction of disparate scales: selective decay by
  Casimir dissipation in fluids - Holm\, D (Imperial College London)
DTSTART:20120823T143000Z
DTEND:20120823T153000Z
UID:TALK39369@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The problem of parameterizing the interactions of disparate sc
 ales in fluid flows is addressed by considering a property of two-dimensio
 nal incompressible turbulence. The property we consider is selective decay
 \, in which a Casimir of the ideal formulation (enstrophy in 2D flows) dec
 ays in time\, while the energy stays essentially constant. This paper intr
 oduces a mechanism that produces selective decay by enforcing Casimir diss
 ipation in fluid dynamics. This mechanism turns out to be related in certa
 in cases to the numerical method of anticipated vorticity discussed in 	te
 {SaBa1981\,SaBa1985}. Several examples are given and a general theory of s
 elective decay is developed that uses the Lie-Poisson structure of the ide
 al theory. A scale-selection operator allows the resulting modifications o
 f the fluid motion equations to be interpreted in several examples as para
 meterizing the nonlinear\, dynamical interactions between disparate scales
 . The type of modified fluid equation systems derived here may be useful i
 n turbulent geophysical flows where it is computationally prohibitive to r
 ely on the slower\, indirect effects of a realistic viscosity\, such as in
  large-scale\, coherent\, oceanic flows interacting with much smaller eddi
 es.\n
LOCATION:Seminar Room 1\, Newton Institute
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