@article{824122,
      recid = {824122},
      author = {Badin, Gualtiero, and Crisciani, Fulvio,},
      title = {Variational formulation of fluid and geophysical fluid  dynamics : mechanics, symmetries and conservation laws /},
      pages = {1 online resource.},
      abstract = {This book describes the derivation of the equations of  motion of fluids as well as the dynamics of ocean and  atmospheric currents on both large and small scales through  the use of variational methods. In this way the equations  of Fluid and Geophysical Fluid Dynamics are re-derived  making use of a unifying principle, that is Hamilton's  Principle of Least Action. The equations are analyzed  within the framework of Lagrangian and Hamiltonian  mechanics for continuous systems. The analysis of the  equations' symmetries and the resulting conservation laws,  from Noether's Theorem, represent the core of the  description. Central to this work is the analysis of  particle relabeling symmetry, which is unique for fluid  dynamics and results in the conservation of potential  vorticity. Different special approximations and relations,  ranging from the semi-geostrophic approximation to the  conservation of wave activity, are derived and analyzed.  Thanks to a complete derivation of all relationships, this  book is accessible for students at both undergraduate and  graduate levels, as well for researchers. Students of  theoretical physics and applied mathematics will recognize  the existence of theoretical challenges behind the applied  field of Geophysical Fluid Dynamics, while students of  applied physics, meteorology and oceanography will be able  to find and appreciate the fundamental relationships behind  equations in this field.},
      url = {http://library.usi.edu/record/824122},
}