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.
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