Motion of a Vortex Filament with Axial Flow in the Half Space

TL;DR

This paper models the motion of a vortex filament with axial flow in a half-space using a nonlinear dispersive equation, proving unique solvability of initial-boundary value problems to analyze tornado dynamics.

Contribution

It introduces a mathematical framework for vortex filament motion with axial flow in a half-space and establishes unique solvability results.

Findings

Proved unique solvability of the initial-boundary value problem.

Developed a nonlinear third order dispersive equation model.

Applied the model to analyze tornado motion.

Abstract

We consider a nonlinear third order dispersive equation which models the motion of a vortex filament immersed in an incompressible and inviscid fluid occupying the three dimensional half space. We prove the unique solvability of initial-boundary value problems as an attempt to analyze the motion of a tornado.