Uma introdução à dinâmica da vorticidade de um fluido newtoniano incompressível com densidade e coeficiente de viscosidade uniformes

Abstract

Vorticity plays a crucial role in the flow regime of a Newtonian fluid, especially in transient and turbulent regimes, where vortices and whirlpools emerge. This thesis analyzes the dynamic equation of vorticity, limited to the case where the fluid's density and viscosity are uniform, revealing how vorticity changes over time. The objective of this work is to provide an introduction to the dynamics of vorticity. The study begins by addressing the treatment of the fluid as a continuous medium, using the continuum hypothesis, kinematics, the types of forces acting on an extended body, and internal friction as the macroscopic representation of the phenomenon of linear momentum transport in the extended body. Next, the fluid is specified through the Eulerian description, leading to the derivation of the equations for the conservation of linear momentum and mass, culminating in the Navier-Stokes equation and the continuity equation, respectively. Finally, equipped to derive the dynamic equation of vorticity, we investigate the terms that contribute to its variation and their individual effects on its distribution.