报告题目：Motion of a magneto-vortex ring with and without Hall effect

报告人：Prof.Fukumoto，日本九州大学

报告时间：2023年12月6日（周三）14:00-15:00

报告地点：21-417

报告摘要：A general formula is established for translation speed of a thin toroidal magnetic eddy in a MHD flow. We start with a review on methods for deriving a general formula for translation speed of an axisymmetric vortex ring, in a viscous fluid, whose core is not necessarily thin. Helmholtz-Lamb's method, developed by Helmholtz, Lamb, Saffman, Rott and Cantwell, provides a short-cut to manipulate the translation speed at both small and large Reynolds numbers, for a vortex ring starting from an infinitely thin core. The resulting asymptotics significantly improve Fraenkel-Saffman's formula (1970) and give closer lower and upper bounds on translation speed in an early stage (Fukumoto & Moffatt 2008, Fukumoto & Kaplanski 2008). At large Reynolds numbers, a further simplification is achieved by Kelvin-Benjamin's kinematic variational principle, a topological idea; a steady distribution of vorticity, relative to a moving frame, is a state of maximum energy, under the constraint of constant hydrodynamic impulse, on an isovortical sheet.Then we adapt these methods to derive a general formula for translation speed of a vortex ring, with toroidal magnetic flux in the core, in the MHD flow. A family of exact solutions is given to Hill's spherical magnetic vortex rings, axisymmetric poloidal MHD flows with purely toroidal magnetic field, with allowance made for the Hall effect. In the absence of the Hall effect, the toroidal magnetic field acts to enhance the traveling speed, but the Hall effect brings the discrepancy in the traveling speed, whether the toroidal magnetic field is parallel or anti-parallel to the toroidal vorticity.

报告人简介：福本康秀，日本九州大学教授，原九州大学应用数学研究所所长。主要研究流体问题和流体动力学。博士毕业于东京大学，日本流体力学学会理事长，日本科学理事会理事，是多个学术杂志的编委，获得过日本人工智能协会创新金奖。

邀请人：张翼