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SUMMARY:Alpha sub-grid scale models of turbulence and inviscid regularizat
 ion - Edriss S. Titi (Weizmann Institute of Science &amp\; University of C
 alifornia - Irvine)
DTSTART:20090514T140000Z
DTEND:20090514T150000Z
UID:TALK18360@talks.cam.ac.uk
CONTACT:6743
DESCRIPTION:In recent years many analytical sub-grid scale models of turbu
 lence\nwere introduced based on the Navier--Stokes-alpha model (also known
 \nas a viscous Camassa--Holm equations or the Lagrangian Averaged\nNavier-
 -Stokes-alpha (LANS-alpha)). Some of these are  the\nLeray-alpha\, the mod
 ified Leray-alpha\, the simplified Bardina-alpha\nand the Clark-alpha mode
 ls. In this talk I will show the global\nwell-posedness of these models an
 d provide  estimates for the\ndimension of their global attractors\, and r
 elate these estimates to\nthe relevant physical parameters. Furthermore\, 
 I will show that up\nto certain wave number in the inertial range the  ene
 rgy power\nspectra of these models obey the Kolmogorov -5/3 power law\, ho
 wever\,\nfor the rest the inertial range the energy spectra are much steep
 er.\n\nIn addition\, I will show that by using these alpha models as closu
 re\nmodels to the Reynolds averaged equations of the Navier--Stokes one\ng
 ets very good agreement with empirical and numerical data of\nturbulent fl
 ows for a wide range of huge Reynolds numbers in\ninfinite pipes and chann
 els.\n\nIt will also be observed that\, unlike the three-dimensional Euler
 \nequations and other inviscid alpha models\, the inviscid simplified\nBar
 dina model has global regular solutions for all initial data.\nInspired by
  this observation I will introduce new inviscid\nregularizing schemes for 
 the three-dimensional Euler\, Navier–Stokes\nand MHD equations\, which d
 oes not require\, in the viscous case\, any\nadditional boundary condition
 s. This same kind of inviscid\nregularization is also used to regularize t
 he Surface\nQuasi-Geostrophic model.\n\nFinally\, and based on the alpha r
 egularization I will present\, if\ntime allows\, some error estimates for 
 the rate of convergence of the\nalpha models to the Navier–Stokes equati
 ons\, and will also present\nnew approximation of vortex sheets dynamics.
LOCATION:MR14\, CMS
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