Formulação Lagrangeana para um fluido compressível - geração de helicidade e vorticidade

Abstract

Alternative formulations for the description of fluid dynamics have been shown to be of major importance. From these last ones, we call attention to the Maxwell-type set of equations, which have as main variables the vorticity and the Lamb vector in the fluid description, since they make possible a mathematical structure analogous to Maxwell's equations in vacuum for classical electromagnetism. In this work, we will present the Maxwell equation system, as well as the derivation of the covariant representation for the fluid. We will address the case of a fluid initially compressible and viscous, and after that, a charged one. Finally, we present the evolution of the circulation and the helicity of the fluid, with the intention of identifying its sources, where we present a new term related to the generation of helicity which does not appear in the specialized literature.