Cavallini F., Crisciani F. Quasi-Geostrophic Theory of Oceans and Atmosphere: Topics in the Dynamics and Thermodynamics of the Fluid Earth

Springer, 2013. — 394 p.
In this book, a detailed derivation of quasi-geostrophic fluid dynamics is given by means of an almost exclusively analytical approach, starting from the classical mechanics of fluids and having in mind the behaviour of large-scale currents and winds. Scale analysis, asymptotic expansions and boundary layer techniques are used wherever possible and repeatedly illustrated in different models; at the same time, the vorticity equations, derived at different scales by means of the above cited techniques, are systematically interpreted in terms of the fundamental Ertel’s theorem. Moreover, basic arguments, such as flow energetics or Rossby waves, are discussed in various contexts depending on the assumed stratification of each model. Thus, the application-oriented reader will be able to appreciate the conditions under which quasi-geostrophic models may be safely used.