The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.
Topological hydrodynamics is a young branch of mathematics studying topological
features of flows with complicated trajectories, as well as their applications
to fluid motions. It is situated at the crossroad of hyrdodynamical stability
theory, Riemannian and symplectic geometry, magnetohydrodynamics, theory
of Lie algebras and Lie groups, knot theory, and dynamical systems. Applications
of this approach include topological classification of steady fluid flows,
descriptions of the Korteweg-de Vries equation as a geodesic flow, and
results on Riemannian geometry of diffeomorphism groups, explaining, in
particular, why longterm dynamical weather forecasts are not reliable.
Topological Methods in Hydrodynamics is the first monograph to treat topological,
group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics
for a unified point of view. The necessary preliminary notions both in
hydrodynamics and pure mathematics are described with plenty of examples
and figures. The book is accessible to graduate students as well as to
both pure and applied mathematicians working in the fields of hydrodynamics,
Lie groups, dynamical systems and differential geometry.
