Enstrophy dynamics for flow past a solid body with no-slip boundary condition

TL;DR

This paper investigates how boundary vorticity influences enstrophy dynamics in flows around streamlined bodies, deriving new identities and equations for both Stokes and Navier-Stokes systems.

Contribution

It introduces a novel energy identity involving boundary vorticity and establishes enstrophy dissipativity and dynamics equations for flow systems.

Findings

Derived a new energy identity including boundary vorticity values.

Proved enstrophy dissipativity for the Stokes system.

Obtained a new enstrophy dynamics equation for the Navier-Stokes system.

Abstract

In the paper we study the impact of the boundary vorticity distribution on the dynamics of enstrophy for flows around streamlined body. A new energy identity is derived in the article, which includes the boundary values of the vortex function. For the Stokes system the dissipativity of enstrophy is proved. For the Navier-Stokes system a new equation of the enstrophy dynamics is obtained.