Self-similar axisymmetric flows with swirl

TL;DR

This paper investigates self-similar solutions to the axisymmetric Navier-Stokes equations with swirl, modeling tornado-like vortices, and explores the existence of explicit solutions and discontinuities.

Contribution

It introduces explicit stationary solutions for zero viscosity and analyzes the non-existence of slip discontinuities in this self-similar framework.

Findings

Explicit solutions for zero viscosity case.

Non-existence of slip discontinuities.

Characterization of flow structures compatible with self-similarity.

Abstract

We consider an infinite vortex line in a fluid which interacts with a boundary surface as a simplified model for tornadoes. We study self-similar solutions for stationary axisymmetric Navier-Stokes equations and investigate the types of motion which are compatible with this structure when viscosity is non-negative. For viscosity equal to zero, we construct a class of explicit stationary solutions. We then consider solutions with slip discontinuity and show that they do not exist in this framework.