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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Vortex dynamics on the surface of a torus - Takash
i Sakajo (Kyoto University\; Kyoto University)
DTSTART;TZID=Europe/London:20191101T113000
DTEND;TZID=Europe/London:20191101T123000
UID:TALK133591AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/133591
DESCRIPTION:As theoretical models of incompressible flows aris
ing in engineering and geophysical problems\, vort
ex dynamics is sometimes considered on surfaces th
at have various geometric features such as multipl
y connected domains and spherical surfaces. The mo
dels are derived from the streamline-vorticity for
mulation of the Euler equations. In order to solve
the model equations\, complex analysis and its co
mputational techniques are effectively utilized. I
n the present talk\, we consider vortex dynamics
on the surface of a torus. Although the flows on t
he surface of a torus is no longer a physical rele
vance to real fluid flow phenomena\, it is theoret
ically interesting to observe whether the geometri
c nature of the torus\, i.e.\, a compact\, orienta
ble 2D Riemannian manifold with non-constant curva
ture and one handle\, yields different vortex dyna
mics that are not observed so far. The vortex mode
l is not only an intrinsic theoretical extension i
n the field of classical fluid mechanics\, but it
would also be applicable to modern physics such as
quantum mechanics and flows of superfluid films.
Based on the model of point vortices\, where the v
orticity distribution is given by discrete delta m
easures\, we investigate equilibrium states of poi
nt vortices\, called vortex crystals\, moving in t
he longitudinal direction without changing their r
elative configuration. Moreover\, we derive an ana
lytic solution of a modified Liouville equation on
the toroidal surface\, where the vorticity distri
bution is given by an exponential of the stream-fu
nction. The solution gives rise to a vortex crysta
l with quantized circulations embedded in a contin
uous vorticity distribution in the plane\, which c
orresponds to a model of shear flows in the plane
known as Stuart vortex. A part of the results pres
ented in this talk is based on the joint works wit
h Mr. Yuuki Shimizu\, Kyoto University.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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