The Effect Of Radiation Velocity Potentials On The Drift Force On A Submerged Sphere
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S. H. Mousavizadegan & M. Rahman
The effect of the motion of a submerged sphere on the horizontal drift force is investigated analytically. The multipole expansion method is used to derive analytical solutions for the diffraction and radiation velocity potentials in a series of associated Legendre functions. The second-order steady force is obtained by the far field method. The effect of all velocity potentials is taken into account in derivation of the horizontal drift force. The total contribution of the radiation velocity potential is minimal to the horizontal drift force if the center of mass is at a distance less than twenty percent of the radius from the center of the sphere. The effect of the radiation velocity potential in vicinity of the resonant frequency is augmented and may create a relatively large horizontal drift force. Keywords: drift forces, radiation, diffraction, multipole expansion. 1 Introduction Marine structures are usually designed to operate in a wave environment. Structural loading of the body surface under the water and unsteady motions of the body are two of the principal resulting problems. When the characteristic body dimension is comparable to the wave length, the potential effects dominate. The presence of the body alters the pattern of wave propagation in the vicinity of the structure and causes wave scattering. The body may also oscillate and cause the radiation of waves if the constraints are not sufficiently rigid. As a consequence, the body experiences reacting forces from the surrounding fluid and constraints. Due to the complexity of the associated boundary value problems with the wavebody interactions in the frame of the potential flow theory, analytical solutions can be obtained for a few special geometries. In general, a numerical solution of Laplace’s equation along with the associated boundary conditions is imperative.
drift forces, radiation, diffraction, multipole expansion.