Introduction to Theoretical and Mathematical Fluid Dynamics

This book features an overview of fluid dynamics from a mathematical viewpoint, intorudces readers to the mathematical study of fluid behavior, and highlights active areas of research in fluid dynamics. Highlighting advances in the field from the past 15 years, tcomprehensive and foundational coverage of theoretical and mathematical fluid dynamics is provided with a focus on incompressible and compressible fluid dynamics. Written by a well-known author and researcher in the field, the book has been extensively classroom-tested and is appropriate for students majoring in mathematics, engineering, and physics alike. Practical applications are included to illustrate the concepts, and plentiful exercises and examples are presented throughout for further study. While mathematically rigourus, the author's clear and explanatory approach aids in reader comprehension of the overall framework of theoretical fluid dynamics. Topical coverage includes: Introduction to the Fluid Model; Equations of Fluid Flows; Hamiltonian Formulation of Fluid Flows; Surface Tension Effect; Fluid Kinematics and Dynamics; The Complex-Variable Metho; Three-Dimensional Irrotational Flow; Vortex Flow; Rotating Flow; Water Wave; Dynamics of Compressible Fluid Flow; Review of Thermodynamic; Isentropic Fluid Flow; Potential Flow; Nonlinear Theory of Plane Sound Wave; Shock Wave; and The Hodograph Method.