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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Equilibrium state of quasi-geostrophic point vorti
ces - Miyazaki\, T (Electro-Communications\, Japan
)
DTSTART;TZID=Europe/London:20081211T113000
DTEND;TZID=Europe/London:20081211T120000
UID:TALK15626AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/15626
DESCRIPTION:The statistics of quasi-geostrophic point vortices
is investigated theoretically and numerically\, i
n order to understand fundamental aspects of quasi
-geostrophic turbulence. Numerical simulations of
N-vortex system (N = 2000 − 8000) in an infinite f
luid domain are performed using a fast special-pur
pose computer (MDGRAPE-3) for molecular dynamics s
imulations.[1] The vortices of the same strength a
re initially located randomly and uniformly in a c
ubic box\, and we choose the state with the highes
t multiplicity for fixed angular momentum. The axi
-symmetric equilibrium state is obtained after abo
ut 20 turn over time. The probability density dist
ribution of the center region resembles that of th
e purely two-dimensional point vortices. The three
-dimensional effect appears near the upper and low
er lids in the tighter concentration of vortices a
round the axis of symmetry (End-effect). The most
probable vortex distributions are determined based
on the maximum entropy theory.[2] We search for t
he state of maximum Shanon-entrophy under the cons
traints of vertical vorticity distribution\, angul
ar momentum and energy (mean-field approximation).
The theoretical predictions agree quite well with
the numerical results.[3] We investigate the infl
uence of energy on the equilibrium state\, in some
detail. Larger vortex clouds have lower energy\,
larger entropy and lager angular momentum. Each ve
rtical layer has same contribution to the entropy
and the angular momentum\, whereas the center regi
on has stronger influence to the energy than the l
ids. Therefore\, the distribution in the center re
gion expands radially for lower energy and shrinks
for higher energy. In order to keep the angular m
omentum unchanged\, the distribution near the lids
should shrink for lower energy and should expand
for higher energy. References [1] Yatsuyanagi Y.\,
Kiwamoto Y.\, Tomita H.\, Sano M.M.\, Yoshida T.\
, Ebisuzaki. T.: Dynamics of Two-Sign Point Vortic
es in Positive and Negative Temperature States. Ph
ys. Rev. Lett. 94:054502\, 2005 [2] Kida S.: Stati
stics of the System of Line Vortices. J. Phys. Soc
. Jpn. 39(5):13951404\, 1975 [3] Hoshi S.\, Miyaza
ki T.: Statistics of Quasi-geostrophic Point Vorti
ces. FDR (Subbmitting)\, 2008.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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