The Finiteness of vortices in steady incompressible viscous fluid flow

TL;DR

This paper proves that steady incompressible viscous fluid flows in finite domains can only contain a finite number of vortices, using geometric theory and Kolmogorov's length scale.

Contribution

It introduces two novel mathematical approaches to establish the finiteness of vortices in steady incompressible viscous flows.

Findings

Finiteness of vortices proven using geometric theory.

Finiteness demonstrated via Kolmogorov's length scale and diametric disks.

Provides rigorous mathematical proofs for vortex count limitations.

Abstract

In this work, we provide two novel approaches to show that incompressible fluid flow in a finite domain contains at most a finite number vortices. We use a recently developed geometric theory of incompressible viscous flows along with an existing mathematical analysis concept to establish the finiteness. We also offer a second proof of finiteness by roping in the Kolmogorov's length scale criterion in conjunction with the notion of diametric disks.