1. Basic Continuum Mechanics

At all scales, from galaxies to elementary particles, matter is discrete. Yet, the “continuum” paradigm is still of paramount importance, both in theory and in practice. This chapter briefly elucidates this paradox, with emphasis on fluid mechanics, and presents the basic conceptual tools needed to approach heuristically the physics of fluids. Both the Lagrangian and the Eulerian descriptions of motion are introduced. The link between these two descriptions stems from the request that a property of an Eulerian field, at a given point and at a given time, coincides with the corresponding property of the Lagrangian particle that occupies that point at that time. In the Lagrangian framework, the governing equations of fluid mechanics, the vorticity dynamics and the parameterization of turbulence are discussed. Illustrative applications of these results to simple models (e.g. flow in a channel and 2-D breezes) are also given.