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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.
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.
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