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.

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.

In recent decades, it has been recognized that environmental pollution causes serious local and global harmful effects, both to human health and ecosystems, and therefore the protection and restoration of the environment is a matter of great importance. Through the joint efforts of mathematicians, geophysicists and environmentalists, diverse methods for solving varied problems of environmental pollution have been developed. In this text, mathematical methods for analyzing the problems of transport and dispersion of relatively passive pollutants, control of air emissions and remediation of polluted aquatic systems are presented in such form that they are easily understood by undergraduate and graduate students. The application of the adjoint method is emphasized as a way to get dual estimates of average concentrations of different substances. This methodology helps to establish simple variational and linear programming formulations in order to calculate optimal solutions of these problems in the sense that they meet the standards of air quality and cause the minimal variations in the industrial processes or in the environment. This text is primarily intended for scientists, engineers and other professionals working in the field of environmental modeling (transport of air and water pollutants, assessment of pollution levels, optimal control of emission rates from point, line and area sources, the optimal location of a new industrial plant, bioremediation of oil-contaminated aquatic zones, etc.). We hope that this book will be useful for undergraduate and graduate students of engineering sciences and earth sciences as well.