Non-self-conjugate model formulation of the Pekeris boundary problem

• Published in: Doklady earth sciences 2010-10, Vol.434 (2), p.1342-1345
• Main Authors: Kasatkin, B. A., Zlobina, N. V.
• Format: Article
• Language: English
• Subjects: Analysis; Boundaries; Boundary conditions; Boundary layer; Earth and Environmental Science; Earth Sciences; Mathematical models; Oceanology; Waveguides
• ISSN: 1028-334X; 1531-8354
• DOI: 10.1134/S1028334X10100119

The theory of wave processes in layered media developed in classical works [13] is based on the solution of the key boundary problem of hydroacous tic science formulated and solved by Pekeris in [1] for the system: homogeneous fluid layerhomogeneous fluid half space. A characteristic peculiarity of the model formulation suggested in [13] is the fact that boundary conditions at the interface waveguidehalf space are formulated as identical conditions of conti nuity by pressure and normal components of the oscil lation velocity with respect to the horizontal coordi nate (local conditions of (p, vz) continuity), while the model formulation appears self conjugate. As a consequence of the assumed model formulation, the solu tion has the form of diverging waves with a singularity O(r1) for the radial component of the oscillation velocity at the symmetry axis in the half space.