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SUMMARY:How to extract a spectrum from hydrodynamic equations - Dario Vinc
 enzi (CNRS (Centre national de la recherche scientifique))
DTSTART:20220527T130000Z
DTEND:20220527T140000Z
UID:TALK174701@talks.cam.ac.uk
DESCRIPTION:Practical results gained from statistical theories of turbulen
 ce usually appear in the form of an inertial-range power-law energy spectr
 um and a cut-off wave-number. To extract such spectral information from th
 e three-dimensional Navier&ndash\;Stokes equations\, Doering and Gibbon (2
 002) introduced the idea of forming a set of dynamic wave-numbers Kn(t) fr
 om ratios of norms of solutions. The time averages of Kn(t) can be interpr
 eted as the moments of the energy spectrum. Since the &kappa\;n(t) are bas
 ed on Navier&ndash\;Stokes weak solutions\, the mathematical bounds for Kn
 (t) connect empirical predictions of the energy spectrum with the analysis
  of the Navier&ndash\;Stokes equations. This method is developed to show h
 ow it can be applied to many hydrodynamic models such as the two dimension
 al Navier&ndash\;Stokes equations (in both the direct- and inverse-cascade
  regimes)\, the forced Burgers equation and shell models.
LOCATION:Seminar Room 2\, Newton Institute
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