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Full Description
This book presents new research on the mathematical description of tsunamis and hurricanes. The description includes dissipative terms and does not contain singularities or two valued functions. The book uses the equivalence principle of solutions of nonlinear large gas dynamic waves and of solutions of water wave equations. An extension of the continuity equation by a source term due to evaporation rates of salt seawater help to understand hurricanes. Detailed formula, tables, and results of the calculations are given.
Contents
From the contents:
Introduction to wave physics: Types of waves; Linear wave equations; Solutions of linear wave equations; Nonlinear wave equations; Physics of nonlinear wave equations.- Basic flow equations: Units and properties of substances; Conservation of mass; The equation of motion; Conservation of energy; Thermodynamics; Vorticity theorems; Potential flow in incompressible fluids; Potential flow in compressible fluids; The DARBOUX solution of plane waves in non-dissipative gases; The equivalence theorem.- Water waves: The variety of water waves; Gravity water waves; Capillarity waves; Solitons; Dissipationless tsunamis; Wave equation for dissipative tsunamis; The tsunami wave equations.- Hurricanes: Terminology and basics; The excitation of vorticity in cyclones; Mathematical modelling of cyclones; Multifluid cyclone modelling.- References.- Index.
