David G. Dritschel教授（Mathematical Institute, University of St Andrews, UK）によるSGU　Special　Lecturesが下記の要領で行われます。興味がある方はぜひお越しください。

日時： 11月17日（火）15:00 - 17:00
場所： 理学研究科 ３号館 1階127室

題目: Long-Time Chaotic Five-Vortex Condensates for Two-Dimensional Euler Flows on a Sphere
概要:
For unforced inviscid flow on the surface of a sphere, statistical mechanical theories fail to capture the long-time flow behaviour known as a “condensate.” In particular, vortices that emerge from prescribed initial vorticity fields do not explore all possible regions of phase space, indicating a lack of ergodicity.

When the total vector angular momentum is zero, numerical simulations have often shown the emergence of four vortices—two cyclonic and two anticyclonic—from initial vorticity fields composed of low- to moderate-degree spherical harmonics.

Here, we demonstrate that five or more vortices can emerge and persist indefinitely, despite undergoing chaotic motion. We investigate the dynamics of five point (singular) vortices and show that a sufficiently tight cluster of three vortices may never separate, even while interacting chaotically with two more distant vortices. The time reversibility of the underlying Hamiltonian system then implies that such tight clusters cannot form from widely separated configurations. Thus, the vortices remain separated by a finite distance for all time. For the continuous Euler equations, this distance can be arbitrarily large compared with a characteristic vortex radius.