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SUMMARY:Linear turbulent cascades
DTSTART:20231017T120000Z
DTEND:20231017T130000Z
DTSTAMP:20260610T152500Z
UID:indico-event-10575@indico.math.cnrs.fr
DESCRIPTION:Speakers: Geoffrey Beck (INRIA Rennes)\n\nTurbulent cascades c
 haracterize the transfer of energy injected by a random force at large sca
 les towards the small scales. In hydrodynamic turbulence\, when the Reynol
 ds number is large\, the velocity field of the fluid becomes irregular and
  the rate of energy dissipation remains bounded from below even if the flu
 id viscosity tends to zero. A mathematical description of the turbulent ca
 scade is a very active research topic since the pioneering work of Kolmogo
 rov in hydrodynamic turbulence and that of Zakharov in wave turbulence. In
  both cases\, these turbulent cascade mechanisms imply power-law behaviors
  of several statistical quantities such as power spectral densities. We ha
 ve constructed a linear equation that mimics the phenomenology of energy c
 ascades when the external force is a statistically homogeneous and station
 ary stochastic process. In the Fourier variable\, this equation can be see
 n as a linear transport equation\, which corresponds to an operator of deg
 ree 0 in physical space. Our results give a complete characterization of t
 he solution: it is smooth at any finite time\, and\, up to smaller order c
 orrections\, it converges to a fractional Gaussian field at infinite time.
  This a bjoint work with Charles-Edouard Bréhier\, Laurent Chevillard\, I
 sabelle Gallagher\, Ricardo Grande and Wandrille Ruffenach.\n\nhttps://ind
 ico.math.cnrs.fr/event/10575/
LOCATION:Fokko du Cloux (Bâtiment Braconnier\, La Doua)
URL:https://indico.math.cnrs.fr/event/10575/
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