近平行涡丝平均场论的精确解
Exact solution to a nearly parallel vortex filament mean-field theory
摘要：
近平行涡丝是点涡的一种推广，它描述了角动量守恒下的许多现象，包括深海对流、磁约束等离子体和太阳大气中形成的涡。虽然点涡代表完全直的、平行的环流线，但由于内部粘性，几乎平行的涡丝具有一定的曲率。它们以几何学的方式相互作用，但也有一个动能自能。在这封信中，我提出了一个精确的解决方案下的角动量守恒的平均场论的这些细丝系统。我证明了细丝具有点涡模型中不存在的无限级相变。
英文摘要：
Nearly parallel vortex filaments are a generalization of point vortices and describe many phenomena under conservation of angular momentum including vortices forming in deep ocean convection, magnetically confined plasmas, and the solar atmosphere. While point vortices represent perfectly straight, parallel lines of circulation, nearly parallel vortex filaments have some curvature due to internal viscosity. They interact logarithmically but have a kinetic self-energy as well. In this letter, I present an exact solution of a system of these filaments under angular momentum conservation in a mean-field theory. I show that the filaments have an infinite order phase transition not present in the point vortex model.
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