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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.
List of contents
Chapter 01- Introduction.- Chapter 02- Spaces of Functions on a Sphere.- Chapter 03- Solvability of Vorticity Equation on a Sphere.- Chapter 04- Dynamics of Ideal Fluid on a Sphere.- Chapter 05- Stability of Rossby-Haurwitz (RH) Waves.- Chapter 06- Stability of Modons and Wu-Verkley waves.- Chapter 07- Linear and Nonlinear Stability of Flows.- Chapter 08- Numerical Study of Linear Stability.- References.
About the author
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.
Summary
Presents a selection of problems on the dynamics of two-dimensional viscous and ideal incompressible fluid on a rotating sphere, combining theoretical, analytical and numerical approaches
Employs an analysis of vortex dynamics on a sphere, which offers a more natural approach for meteorological applications.
Focuses on methods that can be applied to problems in physics, hydrodynamics, meteorology and geophysics
Additional text
“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)
Report
"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)
