A mathematical study on the local fluid rotation axis

TL;DR

This paper rigorously proves that the vorticity vector does not represent the true local fluid rotation axis or strength, and introduces the Liutex vector as the correct measure in viscous flows.

Contribution

It provides a mathematical proof identifying the Liutex vector as the true local fluid rotation axis, correcting long-standing misconceptions in classical fluid kinematics.

Findings

Vorticity vector is not the fluid rotation axis.

Vorticity magnitude does not represent rotational strength.

Liutex vector is the true fluid rotation axis.

Abstract

As widely recognized, vortex represents flow rotation. Vortex should have a local rotation axis as its direction and angular speed as its strength. Vorticity vector has been considered the rotation axis, and vorticity magnitude the rotational strength for a long time in classical fluid kinematics. However, this concept cannot stand in viscous flow. This study demonstrates by rigorous mathematical proof that the vorticity vector is not the fluid rotation axis, and vorticity is not the rotation strength. On the other hand, the Liutex vector is mathematically proved as the fluid rotation axis, and the Liutex magnitude is twice the fluid angular speed.