Dynamic Evolution Equations for Isolated Smoke Vortexes in Rational Mechanics

TL;DR

This paper develops dynamic evolution equations for isolated smoke vortexes, providing a semi-empirical framework to understand their behavior in natural phenomena like hurricanes and turbulence.

Contribution

It introduces a novel set of dynamic evolution equations for smoke vortexes based on empirical observations and geometric motion, applicable to viscous fluids and industrial data.

Findings

Formulated geometric motion equations for smoke circles.

Established dynamic evolution equations for stress fields.

Provided approximation equations for viscous fluids.

Abstract

Smoke circle vortexes are a typical dynamic phenomenon in nature. The similar circle vortexes phenomenon appears in hurricane, turbulence, and many others. A semi-empirical method is constructed to get some intrinsic understanding about such circle vortex structures. Firstly, the geometrical motion equations for smoke circle is formulated based on empirical observations. Based on them, the mechanic dynamic motion equations are established. Finally, the general dynamic evolution equations for smoke vortex are formulated. They are dynamic evolution equations for exact stress field and dynamic evolution equations for average stress field. For industrial application and experimental data processing, their corresponding approximation equations for viscous fluid are given. Some simple discussions are made.