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Books > Science & Mathematics > Physics > States of matter > Plasma physics
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Magnetohydrodynamics and Fluid Dynamics: Action Principles and Conservation Laws (Paperback, 1st ed. 2018)
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Magnetohydrodynamics and Fluid Dynamics: Action Principles and Conservation Laws (Paperback, 1st ed. 2018)
Series: Lecture Notes in Physics, 946
Expected to ship within 10 - 15 working days
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This text focuses on conservation laws in magnetohydrodynamics,
gasdynamics and hydrodynamics. A grasp of new conservation laws is
essential in fusion and space plasmas, as well as in geophysical
fluid dynamics; they can be used to test numerical codes, or to
reveal new aspects of the underlying physics, e.g., by identifying
the time history of the fluid elements as an important key to
understanding fluid vorticity or in investigating the stability of
steady flows. The ten Galilean Lie point symmetries of the
fundamental action discussed in this book give rise to the
conservation of energy, momentum, angular momentum and center of
mass conservation laws via Noether's first theorem. The advected
invariants are related to fluid relabeling symmetries - so-called
diffeomorphisms associated with the Lagrangian map - and are
obtained by applying the Euler-Poincare approach to Noether's
second theorem. The book discusses several variants of helicity
including kinetic helicity, cross helicity, magnetic helicity,
Ertels' theorem and potential vorticity, the Hollman invariant, and
the Godbillon Vey invariant. The book develops the non-canonical
Hamiltonian approach to MHD using the non-canonical Poisson
bracket, while also refining the multisymplectic approach to ideal
MHD and obtaining novel nonlocal conservation laws. It also briefly
discusses Anco and Bluman's direct method for deriving conservation
laws. A range of examples is used to illustrate topological
invariants in MHD and fluid dynamics, including the Hopf invariant,
the Calugareanu invariant, the Taylor magnetic helicity
reconnection hypothesis for magnetic fields in highly conducting
plasmas, and the magnetic helicity of Alfven simple waves, MHD
topological solitons, and the Parker Archimedean spiral magnetic
field. The Lagrangian map is used to obtain a class of solutions
for incompressible MHD. The Aharonov-Bohm interpretation of
magnetic helicity and cross helicity is discussed. In closing,
examples of magnetosonic N-waves are used to illustrate the role of
the wave number and group velocity concepts for MHD waves. This
self-contained and pedagogical guide to the fundamentals will
benefit postgraduate-level newcomers and seasoned researchers
alike.
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