Open AccessConvergence of eigenfunction expansions for flexural gravity waves in infinite water depth
Author(s) -
Santanu Koley,
Kottala Panduranga
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2070/1/012006
Subject(s) - eigenfunction , dirac delta function , velocity potential , mathematical analysis , convergence (economics) , boundary value problem , context (archaeology) , green's function , potential theory , mathematics , function (biology) , boundary (topology) , physics , geology , eigenvalues and eigenvectors , quantum mechanics , paleontology , evolutionary biology , economics , biology , economic growth
In the present paper, point-wise convergence of the eigenfunction expansion to the velocity potential associated with the flexural gravity waves problem in water wave theory is established for infinite water depth case. To take into account the hydroelastic boundary condition at the free surface, a flexible membrane is assumed to float in water waves. In this context, firstly the eigenfunction expansion for the velocity potentials is obtained. Thereafter, an appropriate Green’s function is constructed for the associated boundary value problem. Using suitable properties of the Green’s functions, the vertical components of the eigenfunction expansion is written in terms of the Dirac delta function. Finally, using the property of the Dirac delta function, the convergence of the eigenfunction expansion to the velocity potential is shown.