Basic Continuum Mechanics

  • Fabio Cavallini
  • Fulvio Crisciani
Part of the Atmospheric and Oceanographic Sciences Library book series (ATSL, volume 45)


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.


Vortex Tube Current Field Relative Vorticity Material Element Hydrostatic Equilibrium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Fabio Cavallini
    • 1
  • Fulvio Crisciani
    • 2
  1. 1.Ist. Naz. di Oceanografia e di Geofisica Sperimentale – OGS Geofisica della Litosfera (GDL)SgonicoItaly
  2. 2.Dipartimento di FisicaUniversità di TriesteTriesteItaly

Personalised recommendations