Basic Fluid Dynamics

Abstract

As already stressed in Chapter I, the validity of the Navier-Stokes equations in describing the phenomenon of turbulence in fluids is no longer a topic for serious debate. We will recall in this chapter the basic equations of fluid mechanics and the dynamics of vorticity, with the possible influence of a solid-body rotation ${\vec Omega_n }$, due for instance to the rotation of the Earth (when one considers the motion of oceans or atmosphere. We will discuss the approximation of incompressibility for the velocity field, which will be used in most of this book: it will allow us to discard the acoustic waves, but will take into consideration various heated or stably density-stratified flows. The Boussinesq approximation, in particular, allows one to study the effects of buoyancy. The reader is referred to numerous textbooks (see e.g. Batchelor, 1967, Gill, 1982) for the complete derivation of these equations.