Nonlinear instabilities of spar platforms in waves

Spars are widely recognized as an excellent choice for deep water applications due to their hydrodynamic characteristics. However, some relatively recent works report the occurrence of large motions in the plane perpendicular to wave incidence direction, i.e., not directly excited by waves. These unstable motions have been attributed to Mathieu instabilities, caused by pure hydrostatic variations of the underwater hull geometry. Based on a new approach developed by the Authors for predicting parametric rolling in ships, this nonlinear phenomenon has been investigated for spar platforms. The proposed approach demonstrates analytical and numerically that unstable motions, in fact, may appear, but the mechanism that triggers parametric rolling is not related to variations in the hull hydrostatic characteristics. Nonlinear pressure variations induced by waves passing along the spar introduce parametric excitation. Different from typical ship forms, where this effect is negligible even in very long waves due to shorter draughts, in spars, this excitation can be significant, especially for very long waves. The present paper presents the analytical expressions for roll parametric excitation in spars and numerically explores the proposed approach applied to a typical spar under a wide range of wave heights and periods. Parametric Amplification Domains (PADs) were numerically computed, showing not only the boundaries of the instability regions but also the maximum roll amplitudes.