Fundamental Equations of Fluid and Geophysical Fluid Dynamics

Abstract

The motion of fluids from the smaller to the large scales, i.e. until the oceans and atmospheric currents, is described by a complex interplay of the momentum equations and the equations describing the thermodynamics of the specific system. The resulting set of equations constitutes the branch of physics and applied mathematics called Fluid and Geophysical Fluid Dynamics. The continuum hypothesis and the governing equations of Fluid and Geophysical Fluid Dynamics in their inviscid form are here synthetically reviewed. Emphasis is given to the conservation of energy, enstrophy and potential vorticity, which are written in various approximations. The obtained relationships constitute the basis for the development of the following chapters. Chapter 1 aims thus to give only a résumé of the aspects of Fluid and Geophysical Fluid Dynamics which will be considered from the Lagrangian and Hamiltonian point of view in the other chapters. For this reason, several steps in deriving the governing equations are omitted and only the outlines are mostly reported.