A geometric algebraic approach to fluid dynamics

Abstract

Geometric algebra plays a major role in merging the physical and mathematical ideas in the context of various physical systems. In this paper, we explore certain properties associated with barotropic and non-barotropic fluid flows with the help of geometric algebra over a four-dimensional Euclidean space time manifold. We introduce the concepts of multivectors associated with vorticity, helicity, and parity, which evolve from a four-velocity field. In this context, the fluid dynamical analogs of the Poynting theorem, Lorentz force, and Maxwell’s equations are derived. The fluid Maxwell’s equations can be extracted from a single equation.