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CATEGORIES:Applied and Computational Analysis
SUMMARY:Alpha sub-grid scale models of turbulence and invi
scid regularization - Edriss S. Titi (Weizmann Ins
titute of Science &\; University of California
- Irvine)
DTSTART;TZID=Europe/London:20090514T150000
DTEND;TZID=Europe/London:20090514T160000
UID:TALK18360AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/18360
DESCRIPTION:In recent years many analytical sub-grid scale mod
els of turbulence\nwere introduced based on the Na
vier--Stokes-alpha model (also known\nas a viscous
Camassa--Holm equations or the Lagrangian Average
d\nNavier--Stokes-alpha (LANS-alpha)). Some of the
se are the\nLeray-alpha\, the modified Leray-alph
a\, the simplified Bardina-alpha\nand the Clark-al
pha models. In this talk I will show the global\nw
ell-posedness of these models and provide estimat
es for the\ndimension of their global attractors\,
and relate these estimates to\nthe relevant physi
cal parameters. Furthermore\, I will show that up\
nto certain wave number in the inertial range the
energy power\nspectra of these models obey the Ko
lmogorov -5/3 power law\, however\,\nfor the rest
the inertial range the energy spectra are much ste
eper.\n\nIn addition\, I will show that by using t
hese alpha models as closure\nmodels to the Reynol
ds averaged equations of the Navier--Stokes one\ng
ets very good agreement with empirical and numeric
al data of\nturbulent flows for a wide range of hu
ge Reynolds numbers in\ninfinite pipes and channel
s.\n\nIt will also be observed that\, unlike the t
hree-dimensional Euler\nequations and other invisc
id alpha models\, the inviscid simplified\nBardina
model has global regular solutions for all initia
l data.\nInspired by this observation I will intro
duce new inviscid\nregularizing schemes for the th
ree-dimensional Euler\, Navierâ€“Stokes\nand MHD equ
ations\, which does not require\, in the viscous c
ase\, any\nadditional boundary conditions. This sa
me kind of inviscid\nregularization is also used t
o regularize the Surface\nQuasi-Geostrophic model.
\n\nFinally\, and based on the alpha regularizatio
n I will present\, if\ntime allows\, some error es
timates for the rate of convergence of the\nalpha
models to the Navierâ€“Stokes equations\, and will a
lso present\nnew approximation of vortex sheets dy
namics.
LOCATION:MR14\, CMS
CONTACT:
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