Background Material

Abstract

It is assumed that the reader has an elementary knowledge of vector analysis, differential equations and (geophysical) fluid dynamics. To make reading through the chapters 5-7 more comfortable, some background material is included. First, the general equations of motion are presented in section 2.1 to introduce the notation used in the book. There are many textbooks available where these equations are derived and discussed (Pedlosky, 1987; Cushman-Roisin, 1994). In geophysical fluid dynamics and dynamical oceanography, many results are described in terms of vorticity of the flow. In sections 2.2 and 2.3, the mechanisms of vorticity transport and the concept of potential vorticity will be illustrated by examples. It serves as reference on the terminology used in later chapters. The last piece of background material is elementary hydrodynamic stability theory. In section 2.4, Joseph (1976) is followed in a general discussion on stability bounds. Some more mathematical issues are placed in technical boxes and can be skipped on first reading.

The beginning of a framework: mastering the language.

Etude No 5., H. Villa-Lobos