Three-dimensional flow around a submerged body in finite-depth water

Abstract

The three-dimensional fluid flow around an axisymmetric body submerged in a finite-depth fluid is calculated by an analytical/numerical method based on a Green's function formulation. The flow around a submerged axisymmetric body, such as the infinite-fluid analogue of a Rankine body, can be constructed by superposition of a source and a sink along the axis of symmetry. Analytical evaluation is complicated because of the singular Cauchy-type principal-value integrals with infinite and semi-infinite limits. In this study these integrals are evaluated by using a set of adaptive numerical quadratures. This approach is direct, and it does not require an asymptotic expansion. The results for the three-dimensional flow calculations are applied for the evaluation of pressure signatures of several Rankine-type bodies with different Froude numbers. Streamlines were determined by a second-order finite-difference algorithm that follows a fluid particle by solving an appropriate initial-value problem. As expected, the shape distortion from the infinite-fluid Rankine body geometry was significant when the slenderness and the linearity (small-wave elevation and slope) approximations became inappropriate.