Geometrical Reformulation of some Equations of Fluid Mechanics

Abstract

Abstract

The aim of this thesis is to explain some of the connections between fluid

mechanics and differential geometry and to shed light on formulation of

classical fluid mechanics in a differential geometric language. The thesis presents a reformulation of some of the most basic entities

and equations of fluid mechanics, the continuity equation and the

momentum equation of motion, in a modern differential geometric

language using calculus of exterior differential forms on manifold (exterior

calculus). Also, the study investigates the integrability of some fluid

problems from geometrical perspective, with particular attention to the

Euler equations of motion.