Wave diffraction by axisymmetric and nonaxisymmetric prolate spheroid submerged in infinite depth water having surface tension

Article Type

Research Article

Publication Title

Physics of Fluids

Abstract

Our study exploits multipole expansion method based on Havelock's spheroid theorem to investigate the linear hydrodynamic diffraction problem by a stationary fully immersed elongated spheroid (both axisymmetric and nonaxisymmetric case) when the effect of surface tension is present at the free surface. A prolate spheroidal coordinate system is introduced to utilize the symmetry of the body. Havelock's theorem provides explicit relations that help to transform the fundamental Green's function into the specified coordinate system. The prolate spheroidal body is considered to be exposed to monochromatic time-harmonic incident wave field. An approximate form of velocity potential in prolate spheroidal coordinates is obtained to evaluate hydrodynamic loads (both surge and heave forces) exerted on the fixed spheroid. The final solution is derived by using both the incident and diffraction velocity potentials, which are attained by applying the zero-velocity condition on the damped surface of the body. Numerical simulations for the relevant hydrodynamic properties (forces and moment) acting on the body have been graphically depicted against wave numbers by varying surface tension, depth of submergence, wave heading angle, and slenderness-ratio of the spheroidal body. The presence of surface tension has a significant effect on the forces and moment exerted on the spheroidal body.

DOI

10.1063/5.0273734

Publication Date

7-1-2025

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