© 2017

Mathematical Problems of the Dynamics of Incompressible Fluid on a Rotating Sphere


Table of contents

  1. Front Matter
    Pages i-xii
  2. Yuri N. Skiba
    Pages 1-6
  3. Yuri N. Skiba
    Pages 7-41
  4. Yuri N. Skiba
    Pages 79-108
  5. Yuri N. Skiba
    Pages 109-133
  6. Yuri N. Skiba
    Pages 135-156
  7. Yuri N. Skiba
    Pages 157-192
  8. Yuri N. Skiba
    Pages 193-220
  9. Back Matter
    Pages 221-239

About this book


This book presents selected mathematical problems involving the dynamics of a two-dimensional viscous and ideal incompressible fluid on a rotating sphere. In this case, the fluid motion is completely governed by the barotropic vorticity equation (BVE), and the viscosity term in the vorticity equation is taken in its general form, which contains the derivative of real degree of the spherical Laplace operator.

This work builds a bridge between basic concepts and concrete outcomes by pursuing a rich combination of theoretical, analytical and numerical approaches, and is recommended for specialists developing mathematical methods for application to problems in physics, hydrodynamics, meteorology and geophysics, as well for upper undergraduate or graduate students in the areas of dynamics of incompressible fluid on a rotating sphere, theory of functions on a sphere, and flow stability.


Barotropic vorticity equation Incompressible fluid Fluid dynamics Flow stability Rossby-Haurwitz waves Wu-Verkley waves Linear stability M13120 U24005 P19013 P21026

Authors and affiliations

  1. 1.Center for Atmospheric SciencesNational Autonomous University of MexicoMexicoMexico

About the authors

Yuri N. Skiba is a senior researcher at the Center for Atmospheric Sciences, National Autonomous University of Mexico (UNAM), and head of the Mathematical Modeling of Atmospheric Processes group. He holds a PhD in Physics and Mathematics from the Academy of Sciences of the USSR (1979) and a Master in Theoretical Mechanics from the State University of Novosibirsk (1971). He serves as both associate editor and reviewer for several journals. His fields of interest include computational and mathematical modeling, thermodynamic and hydrodynamic modeling, nonlinear fluid dynamics, numerical analysis of PDEs, transport of pollutants, and optimal control of emission rates.

Bibliographic information


“The book contains a deep analysis of mathematical problems of two-dimensional dynamics of an ideal liquid on a rotating sphere and some numerical calculations of the related problems. … This book may be useful for scientists, graduate students, and for all interested in the numerical calculations of dynamics of a liquid on a rotating sphere.” (Oleg A. Sinkevich, zbMATH 1391.76003, 2018)