Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives

Das, Dilip and Mandal, BN and Chakrabarti, A (2008) Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives. In: Fluid Dynamics Research, 40 (4). pp. 253-272.

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Abstract

A modified form of Green's integral theorem is employed to derive the energy identity in any water wave diffraction problem in a single-layer fluid for free-surface boundary condition with higher-order derivatives. For a two-layer fluid with free-surface boundary condition involving higher-order derivatives, two forms of energy identities involving transmission and reflection coefficients for any wave diffraction problem are also derived here by the same method. Based on this modified Green's theorem, hydrodynamic relations such as the energy-conservation principle and modified Haskind–Hanaoka relation are derived for radiation and diffraction problems in a single as well as two-layer fluid.

Item Type:	Journal Article
Publication:	Fluid Dynamics Research
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elsevier Science.
Keywords:	Linear theory;Single and two-layer fluid;Free-surface boundary condition with higher-order derivatives;Energy identities.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	30 Mar 2010 10:57
Last Modified:	19 Sep 2010 05:57
URI:	http://eprints.iisc.ac.in/id/eprint/26288

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