Mathematical Geophysics

An Introduction to Rotating Fluids and the Navier-Stokes Equations
Erscheinungsjahr 2006
ISBN: 978-0-19-857133-9
Verlag: OUP Oxford

Buch, Englisch, Band 32, 264 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 564 g

Reihe: Oxford Lecture Series in Mathematics and Its Applications

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 R². 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.

Autoren/Hrsg.

Chemin, Jean-Yves

Desjardins, Benoit

Gallagher, Isabelle

Grenier, Emmanuel

Fachgebiete

• Geowissenschaften Geologie Geophysik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Populärwissenschaftliche Werke
• Geowissenschaften Geologie Marine Geologie, Ozeanographie (Meereskunde)
• Naturwissenschaften Physik Angewandte Physik Geophysik

Über Autor(innen)

Jean-Yves Chemin is a Professor at the University of Paris VI

Benoit Desjardins is based at the Centre of Atomic Studies centre de Bruyers le Chatel

Isabelle Gallagher is a Professor at the Institut de Mathématiques de Jussieu

Emmanuel Greiner is based at the École Normale Superiore de Lyon