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<p>Klein, Majda, and Damodaran have previously developed a formalized asymptotic motion law describing the evolution of nearly parallel vortex filaments within the framework of the three-dimensional Euler equations for incompressible fluids. In this study, we rigorously justify this model for two configurations: the central configuration consisting of regular polygons of <i>N</i> helical-filaments rotating with constant speed, and the central configurations of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(N+1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> vortex filaments, where an <i>N</i>-polygonal central configuration surrounds a central straight filament.</p>

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Nearly parallel helical vortex filaments in the three-dimensional Euler equations

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • Ignacio Guerra,
  • Monica Musso

摘要

Klein, Majda, and Damodaran have previously developed a formalized asymptotic motion law describing the evolution of nearly parallel vortex filaments within the framework of the three-dimensional Euler equations for incompressible fluids. In this study, we rigorously justify this model for two configurations: the central configuration consisting of regular polygons of N helical-filaments rotating with constant speed, and the central configurations of \(N+1\) N + 1 vortex filaments, where an N-polygonal central configuration surrounds a central straight filament.