WATER ENTRY AND EXIT OF HORIZONTAL CIRCULAR-CYLINDERS

This paper describes fully nonlinear two-dimensional numerical calcula tions of the free-surface deformations of initially calm water caused by the forced motion of totally or partially submerged horizontal circ ular cylinders. The paper considers the following. (i) Totally submerg ed cylinders moving with constant velocity in vertical, horizontal or combined motions. Results are compared with the small-time asymptotic solution obtained by Tyvand & Miloh in 1995. Their results, which are taken to third-order (which is when gravity terms first appear in the expansions), are in excellent agreement with the numerical calculation s for small times; beyond this only the numerical method gives accurat e results until the free surface breaks or the cylinder emerges from t he free surface. Breaking can occur during exit due to strongly negati ve pressures arising on the cylinder surface, or during the downwards motion causing a free-surface depression which closes up rapidly, form ing splashes. Down wards motion is also shown to give rise to high-fre quency waves in some cases. (ii) The free-surface deformations, pressu res and forces acting on a cylinder in vertical or oblique forced moti on during engulfment when it submerges from being initially half-subme rged. The initial stages, when the cylinder still pierces the free sur face, specify the initial conditions for a separate program for a comp letely submerged body, thereby allowing complete engulfment to be stud ied. The free surface closes up violently over the top of the cylinder resulting in jet flow, which, while difficult to handle numerically, has been shown to be insignificant for the bulk flow and the cylinder pressures and forces.