Mathematical Geophysics
An introduction to rotating fluids and the Navier-Stokes equations
Series: Oxford Lecture Series in Mathematics and Its Applications; 32;
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Product details:
- Publisher OUP Oxford
- Date of Publication 13 April 2006
- ISBN 9780198571339
- Binding Hardback
- No. of pages264 pages
- Size 240x160x20 mm
- Weight 540 g
- Language English 0
Categories
Short description:
Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The Navier-Stokes equations are examined in both incompressible and rapidly rotating forms.
MoreLong description:
Aimed at graduate students, researchers and academics in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The text is divided into four parts, with the first part providing the physical background of the geophysical models to be analysed. Part II is devoted to a self contained proof of the existence of weak (or strong) solutions to the incompressible Navier-Stokes equations. Part III deals with the rapidly rotating Navier-Stokes equations, first in the whole space, where dispersion effects are considered. The case where the domain has periodic boundary conditions is then analysed, and finally rotating Navier-Stokes equations between two plates are studied, both in the case of periodic horizontal coordinates and those in R?. In Part IV the stability of Ekman boundary layers, and boundary layer effects in magnetohydrodynamics and quasigeostrophic equations are discussed. The boundary layers which appear near vertical walls are presented and formally linked with the classical Prandlt equations. Finally spherical layers are introduced, whose study is completely open.
...recommended...providing an excellent overview of the technical aspects of Navier-Stokes analysis [and] the physical effects...of rotating flows.
Table of Contents:
Preface
General Introduction
On the Navier-Stokes equations
Some elements of functional analysis
Weak solutions of the Navier-Stokes equations
Stability of the Navier-Stokes equations
References and remarks on the Navier-Stokes equations
Rotating Fluids
Dispersive cases
The periodic case
Ekman boundary layers for rotating fluids
References and remarks on rotating fluids
Perspectives
Stability of horizontal boundary layers
Other systems
Vertical layers
Other layers
References
