Approximate solution of the local induction equation for a conical helical vortex

IF 0.6 4区工程技术 Q4 ENGINEERING, AEROSPACE

Thermophysics and Aeromechanics Pub Date : 2026-04-16 DOI:10.1134/S0869864325010299

P. A. Kuibin

引用次数: 0

Abstract

The work is devoted to finding an approximate analytical solution of the Local Induction Equation describing evolution of the vortex filament of a conical helical form. The solution for the radial coordinate of the filament is presented in implicit quadrature form. Analitical formulas for the two remaining coordinates, angular and axial ones are derived. The found approximate solution provides clear picture of the vortex filament dynamics in dependence on the problem parameters. This sollution allows one to omit the initial period during numerical integration of the Local Induction Equation.

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锥形螺旋涡局部感应方程的近似解

本文致力于寻找描述螺旋形涡丝演化的局部感应方程的近似解析解。以隐式正交形式给出了灯丝径向坐标的解。导出了剩余两个坐标角坐标和轴坐标的解析公式。所得到的近似解提供了涡丝随问题参数变化的清晰图像。该解允许在局部感应方程数值积分时忽略初始周期。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Thermophysics and Aeromechanics THERMODYNAMICS-MECHANICS

CiteScore

0.90

自引率

40.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal Thermophysics and Aeromechanics publishes original reports, reviews, and discussions on the following topics: hydrogasdynamics, heat and mass transfer, turbulence, means and methods of aero- and thermophysical experiment, physics of low-temperature plasma, and physical and technical problems of energetics. These topics are the prior fields of investigation at the Institute of Thermophysics and the Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences (SB RAS), which are the founders of the journal along with SB RAS. This publication promotes an exchange of information between the researchers of Russia and the international scientific community.