Water Waves: The Mathematical Theory with ApplicationsCourier Dover Publications, 17 avr. 2019 - 592 pages First published in 1957, this is a classic monograph in the area of applied mathematics. It offers a connected account of the mathematical theory of wave motion in a liquid with a free surface and subjected to gravitational and other forces, together with applications to a wide variety of concrete physical problems. A never-surpassed text, it remains of permanent value to a wide range of scientists and engineers concerned with problems in fluid mechanics. The four-part treatment begins with a presentation of the derivation of the basic hydrodynamic theory for non-viscous incompressible fluids and a description of the two principal approximate theories that form the basis for the rest of the book. The second section centers on the approximate theory that results from small-amplitude wave motions. A consideration of problems involving waves in shallow water follows, and the text concludes with a selection of problems solved in terms of the exact theory. Despite the diversity of its topics, this text offers a unified, readable, and largely self-contained treatment. |
Table des matières
3 | |
The Two Basic Approximate Theories | 19 |
Subdivision | 37 |
Waves Maintained by Simple Harmonic Surface Pressure | 55 |
CHAPTER PAGE | 58 |
Waves on Sloping Beaches and Past Obstacles | 69 |
Subdivision | 149 |
Subdivision C | 197 |
CHAPTER PAGE | 451 |
Appendix to Chapter 11 Expansion in the neighborhood of the first | 505 |
Problems in which Free Surface Conditions are Satisfied Exactly | 513 |
545 | |
Author Index | 561 |
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Expressions et termes fréquents
amplitude analytic analytic function angle approximate theory approximation assumed assumption asymptotic behaves boundary conditions bounded calculations Chapter coefficients consider const constant coordinate system course curve defined derivatives determined differential equations discontinuity discussion disturbance downstream energy fact finite fixed flood flow follows formula Fourier free surface condition front given harmonic function hence Hölder continuous hydraulic jump indicated infinity initial conditions initial value problem integral mathematical method motion nonlinear numerical observe obtained Ohio order terms oscillations parameter particles plane positive preceding section prescribed pressure progressing waves propagation speed quantities radiation condition real axis region result river satisfies shallow water theory ship shock simple harmonic simple wave singularity slope ſº solitary wave solution solved standing wave stationary front stationary phase steady straight characteristics surface elevation t-plane tion upstream vanishes variables velocity potential vertical wave length yield zero