IMPULSIVE MOTION OF A WIDE TORUS SUBMERGED BELOW A FREE-SURFACE

The impulsively starting motion of a torus submerged horizontally belo w a free surface is studied analytically, using a small-time expansion . The torus is assumed wide, i.e., the torus radius is much larger tha n its initial submergence depth. A quasi-two-dimensional theory is app lied. Its accuracy is checked by comparing the first-order surface ele vation with slender-body theory. The hydrodynamic force and torque are investigated in the first three orders of the small-time expansion. T he ratio between the cross-section radius and submergence depth is arb itrary (between 0 and 1). The general motion of the torus consists of all six degrees of freedom. Special emphasis is put on the five differ ent leading-order nonlinear interactions that may occur between these modes: surge/heave, surge/roll, sway/roll, heave/roll, and roll/yaw. T hese leading-order nonlinear interactions give rise to zeroth-order fo rces and torques. The leading-order gravitational effects are investig ated.