BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Equilibrium state of quasi-geostrophic point vortices - Miyazaki\,
  T (Electro-Communications\, Japan)
DTSTART:20081211T113000Z
DTEND:20081211T120000Z
UID:TALK15626@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The statistics of quasi-geostrophic point vortices is investig
 ated theoretically and numerically\, in order to understand fundamental as
 pects of quasi-geostrophic turbulence. Numerical simulations of N-vortex s
 ystem (N = 2000 − 8000) in an infinite fluid domain are performed using 
 a fast special-purpose computer (MDGRAPE-3) for molecular dynamics simulat
 ions.[1] The vortices of the same strength are initially located randomly 
 and uniformly in a cubic box\, and we choose the state with the highest mu
 ltiplicity for fixed angular momentum. The axi-symmetric equilibrium state
  is obtained after about 20 turn over time. The probability density distri
 bution of the center region resembles that of the purely two-dimensional p
 oint vortices. The three-dimensional effect appears near the upper and low
 er lids in the tighter concentration of vortices around the axis of symmet
 ry (End-effect). The most probable vortex distributions are determined bas
 ed on the maximum entropy theory.[2] We search for the state of maximum Sh
 anon-entrophy under the constraints of vertical vorticity distribution\, a
 ngular momentum and energy (mean-field approximation). The theoretical pre
 dictions agree quite well with the numerical results.[3] We investigate th
 e influence of energy on the equilibrium state\, in some detail. Larger vo
 rtex clouds have lower energy\, larger entropy and lager angular momentum.
  Each vertical layer has same contribution to the entropy and the angular 
 momentum\, whereas the center region has stronger influence to the energy 
 than the lids. Therefore\, the distribution in the center region expands r
 adially for lower energy and shrinks for higher energy. In order to keep t
 he angular momentum unchanged\, the distribution near the lids should shri
 nk for lower energy and should expand for higher energy. References [1] Ya
 tsuyanagi Y.\, Kiwamoto Y.\, Tomita H.\, Sano M.M.\, Yoshida T.\, Ebisuzak
 i. T.: Dynamics of Two-Sign Point Vortices in Positive and Negative Temper
 ature States. Phys. Rev. Lett. 94:054502\, 2005 [2] Kida S.: Statistics of
  the System of Line Vortices. J. Phys. Soc. Jpn. 39(5):13951404\, 1975 [3]
  Hoshi S.\, Miyazaki T.: Statistics of Quasi-geostrophic Point Vortices. F
 DR (Subbmitting)\, 2008.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR