Linear Water Waves: A Mathematical ApproachCambridge University Press, 11 juil. 2002 - 513 pages This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section uses a plethora of mathematical techniques in the investigation of these three problems. The techniques used in the book include integral equations based on Green's functions, various inequalities between the kinetic and potential energy and integral identities which are indispensable for proving the uniqueness theorems. The so-called inverse procedure is applied to constructing examples of non-uniqueness, usually referred to as 'trapped nodes.' |
Table des matières
Basic Theory of Surface Waves | 1 |
Greens Functions | 21 |
Submerged Obstacles | 50 |
Semisubmerged Bodies II | 142 |
Horizontally Periodic Trapped Waves | 214 |
Greens Functions | 265 |
The NeumannKelvin Problem for a Submerged Body | 318 |
TwoDimensional Problem for a SurfacePiercing Body | 361 |
Existence and Properties | 421 |
Bibliography | 485 |
Autres éditions - Tout afficher
Linear Water Waves: A Mathematical Approach N. Kuznetsov,Nikolaĭ Germanovich Kuznet︠s︡ov,Vladimir Gilelevič Mazʹâ,V. Maz'ya,B. Vainberg Aucun aperçu disponible - 2002 |
Expressions et termes fréquents
angle applied arbitrary assertion assume assumption asymptotic axis behavior body bottom boundary boundary condition boundary value problem bounded Chapter condition consider constant contained continuous corresponding cosh cylinder defined demonstrate denote depend depth derivatives described directed dxdy energy equal estimate example existence expansion fact field finite formula free surface frequencies geometries given gives Green's function Hence holds homogeneous identity implies inequality infinite infinity integral equation interval leads method obtained operator positive present proof properties prove representation respectively satisfies shown side sinh smooth solution streamlines submerged Subsection sufficiently surface-piercing symmetric takes tends term theorem theory trapped modes two-dimensional uniquely solvable uniqueness theorem vanishes vertical water domain water-wave problem waves zero ди
Informations bibliographiques
| Titre | Linear Water Waves: A Mathematical Approach |
| Auteurs | Nikolaĭ Germanovich Kuznet︠s︡ov, V. G. Mazʹi︠a︡, B. Vainberg |
| Édition | illustrée |
| Éditeur | Cambridge University Press, 2002 |
| ISBN | 0521808537, 9780521808538 |
| Longueur | 513 pages |
| Exporter la citation | BiBTeX EndNote RefMan |