Rezensionen
Rezensionen
Alexander A. Dorfmann
Green Function Technique For Water Waves
Integral Transforms, Integral Equations, Asymptotics
Rezension
This monograph focuses on the application of Green´s functions for the solution of linear water wave problems. The general water wave problem is formulated in terms of the Laplace equation with (i) boundary conditions at the free surface, at the impermeable bottom and at body surfaces and (ii) radiation conditions at infinity. This general formulation is specified for a number of typical water wave phenomena: wave radiation-diffraction, ship wave propagation, sloshing in containers, wave-current interactions, wave propagation in two-layer fluid systems, and evolution of capillarygravity waves. Most of the analysis is dedicated to constructing representations for the Green´s functions to reduce the above water wave problems into integral equations and to obtain asymptotic representations. The minor weakness of the monograph-i.e. the fairly mathematical approach, which does not give much attention to the physical aspects of the phenomena at hand-is largely redeemed by the clarity of presentation and breadth of applications analyzed. In summary, this very complete compendium on the use of Green´s functions for linear water wave problems represents a useful support for students, practitioners and scientists who face the need of solving varied problems characterized by the evolution of linear water waves. (Maurizio Brocchini)
