Hydrodynamics identities and wave-drift force of a porous body

Wave analysis of porous geometry with linear resistance law

“…A set of relations of the linear force coefficients have by Zhao et al (2011a) been obtained by use of Green's theorem to the set of wave potentials. The relations are generalizations of the usual added mass and damping symmetry and the Haskind-relation in the diffraction problem for solid geometries, where a linear resistance law is assumed for the porous case.…”

“…The symmetry of a ij and b ij was demonstrated by Zhao et al (2011a). The work per unit time performed by the force opposing the pressure force on the body, in the radiation mode J, averaged in time, is expressed by…”

“…In relation to marine and offshore hydrodynamics, Zhao et al (2011a) developed generalizations of the common expressions of the linear radiation and diffraction forces as well as obtaining the mean drift force, where calculations were obtained for a vertical truncated cylinder assuming normal mode expansions of the external and internal wave potentials. In Zhao et al (2011b) they obtained experimental relations between the porosity factor and the opening fraction of the geometry, in combination with the wave slope of the incoming waves.…”

“…In the present paper, the main novelties, for a porous geometry located in the free surface, assuming a linear resistance law, include: a) a wave analysis of porous geometries of arbitrary shape; b) a formulation based on integral equations valid for bodies in three dimensions; c) numerical representation and calculation of the various force coefficients of the general body including the energy balance; d) particular efforts obtaining the linear exciting force and mean drift force where the latter is second order in the wave amplitude; e) practical evaluation of these quantities, where the exciting force and mean drift force are important quantities in a wave analysis of floating fish farms, for example. The evaluation of the mean drift force on the porous geometry -of arbitrary shape -is a particular novel contribution, since none of the above mentioned publications have considered this force, or its numerical values have been obtained erroneously as in Zhao et al (2011a). Thus, particularly, section 5 of the paper is devoted to the evaluation of the mean drift force.…”

“…Section 4 describes the linear forces including added mass, damping and the exciting forces, as well as the energy relation, and their numerical evaluation. In section 5 we rederive the mathematical expression for the mean horizontal drift force and perform numerical calculations for solid and porous geometries with comparison to existing publications for the solid body case (Grue and Biberg, 1993;Molin, 1994) as well as for the porous body case (Zhao et al, 2011a) correcting the numerical calculations in the latter for an obvious error. Finally section 6 is a conclusion.…”