Hydrodynamic coefficients for a floating semi-porous compound cylinder in finite ocean depth

Abstract

Employing the methods of separation of variables and matched eigenfunction expansions for velocity potential, analytical solutions are proposed for a water wave radiation problem of a floating semi-porous compound cylinder in finite ocean depth. The configuration of the semi-porous compound cylinder is such that it consists of an impermeable inner cylinder rising above the free surface and a coaxial truncated porous cylinder around the lower part of the inner cylinder with the top of the porous cylinder being impermeable. The condition on the porous boundary is defined by applying Darcy's law as in Williams et al. (Ocean Eng 27:1-28, 2000). The translational motions in the x-and z-directions, i.e., surge and heave motions, are investigated. A mathematical model is developed which can be considered as an extension of a number of the earlier works, e.g.,

Theoretical Hydrodynamic Analysis of a Surface-Piercing Porous Cylindrical Body

“…The exciting moments behave reversely. Similar resonance phenomenon due to sloshing can be also observed in the works of [40,64].…”

“…Furthermore, wave forces on porous geometries with linear and quadratic resistance laws were presented in [36,37], whereas in [38] the image method was applied to study the effect of a vertical breakwater on the hydrodynamics of a bottom-mounted surface-piercing porous cylinder placed in front of the wall. Recently, the diffraction and radiation problems of a semi-porous truncated cylinder in finite water depth was solved in [39][40][41], employing the method of the separation of variables and matched eigenfunction expansions for the velocity potentials around the cylinder. Additionally, in [42] a boundary element method model was presented on structures composed of solid and porous surfaces applying a linear or quadratic pressurevelocity relation, whereas an efficient method to remove irregular frequencies in the waveporous structure interactions based on the null-field approach was presented in [43].…”

Mean Drift Wave Forces on Arrays of Bodies Surrounded by Thin Porous Surfaces

“…and a radiation condition which states that propagating disturbances must be outgoing [47]. Furthermore, since a fine-pore assumption is applied, ϕ p,n D must satisfy the boundary condition on the porous cell [36,48]:…”

“…In Equation ( 6), the term G stands for the dimensionless complex porosity coefficient. The coefficient can be written as: G = G R + iG I , where G R represents the linearized drag effect of the porous surface, and G I represents the inertia effect [36]. Furthermore, G also measures the porosity of the porous surface.…”

“…Here, the Haskind relations were applied, and an additional damping coefficient due to the porosity was found. Furthermore, a hydrodynamic analysis of a single surface-piercing, semi-porous compound cylinder, employing the methods of separation of variables and matched eigenfunction expansions for the velocity potential, was presented in [34][35][36]. It was found that an appropriate optimal ratio of various parameters such as radius, draught, and porosity can be established for to minimize the adverse hydrodynamic effects on the structure.…”