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.

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.