Three vortex shedding modes, i.e. independent vortex shedding, interactive vortex shedding and uni-directional vortex shedding, for flow induced by oscillatory vertical cylinder witha disk attached at its keel were presented in Part I. The occurrence of these modes were shown to depend on the Keulegan-Carpenter (KC) number and disk thickness-diameter ratio. Associated with these distinct changes of vortex shedding patterns are distinct increases in the hydrodynamic damping. A quantitative method of identifying the vortex shedding flow regimes is proposed, and the scaling laws for heave damping estimation of cylinder + disk configuration are presented. A sample calculation on a classic Spar platform show that addition of a heave plate increased the heave damping fourfold. (C) 2003 Elsevier Ltd. All rights reserved.