理想流体中定常自由涡环运动

STEADY FREE VORTEX RINGS IN AN INVISCID FLUID

摘要

摘要:本文研究理想均质不可压缩无界流体中的轴对称定常涡环运动。通过对柱坐标系下的定常Euler方程的高精度数值求解,给出了求涡核区有任意涡量分布情况下轴对称定常涡环解的方法,并就涡环的运动特性进行了讨论,其极限情况与已有的理论解完全一致。在此基础之上,还发展了一种柱坐标系下以傅氏级数为基函数作展开的高效谱方法,成功地解决了奇性(r=0)问题。

Abstract:Axisymmetric vortex rings which move steadily through an incompressible unbounded ideal fluid at rest at infinity are investigated. A general spectral scheme is proposed for seeking solutions of steady axisymmetric vortex rings with arbitrary vorticity distribution in the core. The properties of vortex ring are also given a numerical description. Comparison between the numerical results and asymptotic analytic solution is very satisfactory.