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CATEGORIES:DAMTP Astrophysics Seminar
SUMMARY:Statistical averaging\, smoothing and filtering -
Prof. Anvar Shukurov (Newcastle)
DTSTART;TZID=Europe/London:20190218T140000
DTEND;TZID=Europe/London:20190218T150000
UID:TALK115453AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/115453
DESCRIPTION:Theory of turbulence is based on ensemble averagin
g\, but this type of averaging is not practical in
most laboratory measurements\, astronomical obser
vations and numerical simulations as it requires v
ery large number of independent realisations of ra
ndom fields involved. An alternative\, widely used
in many applications\, and indeed the only one po
ssible in astronomy\, is the smoothing or filterin
g of random fields (in fact the output of any astr
onomical instrument is a smoothed or filtered phys
ical field). However\, spatial (or temporal) smoot
hing or filtering do not satisfy the Reynolds rule
s of averaging. Similarly\, modern numerical simul
ations of turbulent flows are performed in spatial
and temporal domains of a relatively small size a
nd ensemble averaging is out of question. Thus\, a
nalyses of such numerical simulations employ vario
us averages (such as plane averages) that satisfy
the Reynolds rules. However\, such averages can be
physically inappropriate\, e.g.\, when the mean q
uantities do not need to be independent of any spa
tial coordinates. We discuss the approach to spati
al smoothing and filtering that allows one to avoi
d this difficulty and to derive consistently avera
ged quantities and equations that retain a full 3D
structure.
LOCATION:MR14\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:Dr William Béthune
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