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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Fluid Mechanics - A Geometrical Point of View (Hardcover)
Loot Price: R2,234
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Fluid Mechanics - A Geometrical Point of View (Hardcover)
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Fluid Mechanics: A Geometrical Point of View emphasizes general
principles of physics illustrated by simple examples in fluid
mechanics. Advanced mathematics (e.g., Riemannian geometry and Lie
groups) commonly used in other parts of theoretical physics (e.g.
General Relativity or High Energy Physics) are explained and
applied to fluid mechanics. This follows on from the author's book
Advanced Mechanics (Oxford University Press, 2013). After
introducing the fundamental equations (Euler and Navier-Stokes),
the book provides particular cases: ideal and viscous flows,
shocks, boundary layers, instabilities, and transients. A
restrained look at integrable systems (KdV) leads into a
formulation of an ideal fluid as a hamiltonian system. Arnold's
deep idea, that the instability of a fluid can be understood using
the curvature of the diffeomorphism group, will be explained.
Leray's work on regularity of Navier-Stokes solutions, and the
modern developments arising from it, will be explained in language
for physicists. Although this is a book on theoretical physics,
readers will learn basic numerical methods: spectral and finite
difference methods, geometric integrators for ordinary differential
equations. Readers will take a deep dive into chaotic dynamics,
using the Smale horse shoe as an example. Aref's work on chaotic
advection is explained. The book concludes with a self-contained
introduction to renormalization, an idea from high energy physics
which is expected to be useful in developing a theory of
turbulence.
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