Convergence of Eigenfunction Expansions for Membrane Coupled Gravity Waves
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In the present paper, some characteristics of eigenfunctions associated with membrane coupled gravity waves and its convergence are provided for finite water depth. Expansion formulae for velocity potentials and related orthogonal mode coupling relations for Laplace equation subject to the higher order boundary conditions are studied. The spectral representation of eigenfunctions is obtained in terms of Dirac delta function through the Green’s function technique. Finally, the convergence of eigenfunction expansion to velocity potential is obtained with the help of spectral representations.
KeywordsSpectral representation Green’s function technique Convergence of eigenfunction expansion
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