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

1. Front Matter

   Pages i-xii

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2. Introduction

   • Yuri N. Skiba

   Pages 1-6

3. Spaces of Functions on a Sphere

   • Yuri N. Skiba

   Pages 7-41

4. Solvability of Vorticity Equation on a Sphere

   • Yuri N. Skiba

   Pages 43-77

5. Dynamics of Ideal Fluid on a Sphere

   • Yuri N. Skiba

   Pages 79-108

6. Stability of Rossby-Haurwitz (RH) Waves

   • Yuri N. Skiba

   Pages 109-133

7. Stability of Modons and Wu-Verkley Waves

   • Yuri N. Skiba

   Pages 135-156

8. Linear and Nonlinear Stability of Flows

   • Yuri N. Skiba

   Pages 157-192

9. Numerical Study of Linear Stability

   • Yuri N. Skiba

   Pages 193-220

10. Back Matter

    Pages 221-239

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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.

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

“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)

• Center for Atmospheric Sciences, National Autonomous University of Mexico, Mexico, Mexico

  Yuri N. Skiba

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.

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