Analysis of Peak Mooring Forces Caused by Slow Vessel Drift Oscillations in Random Seas
Authors: Hsu F.H. , Blenkarn K.A. 
Published: December 2007

Abstract
A procedure for calculation of peak mooring force caused by the long-period vessel drift oscillation is described. The long-period drift oscillation is induced by the action of groups of high waves in random seas. The procedure is developed from consideration of momentum flux change in ocean waves.

Introduction
The demand on the offshore petroleum industry for mooring under trying conditions has created the need for a clearer understanding of the physical phenomena involved in mooring large vessels under phenomena involved in mooring large vessels under severe conditions in the open ocean. The offshore industry has experienced major difficulties in mooring under storm conditions and has suffered extensive financial loss. Over the years, attempts have been made to solve offshore mooring problems, utilizing a variety of vessels and mooring techniques. Results of experience and practice offer conflicting indications of the relative merits of various mooring systems. Various engineering and scientific studies have contributed toward an understanding of many factors influencing forces; however, it appears that previous studies have, for the most part, ignored an important phenomenon, which under certain situations is the governing factor to be considered in design of mooring systems. Specifically, there has been little attention devoted to the effects of slow vessel drift oscillations in random or irregular seas. It is this phenomenon that is the prime subject of the present phenomenon that is the prime subject of the present paper. paper. Fig. 1 illustrates results obtained from model tests of a moored vessel in irregular waves. Shown in the figure, as a function of time, are the variations of wave height and period, the surge or drift position of the vessel, and the tension in the primary mooring line. It will be noted that the surge primary mooring line. It will be noted that the surge motion of the vessel involves both a direct wave-induced short-period surge and a gradual long-period drift oscillation taking place over a period of 1 minute or more in prototype time. This type of drift motion is also found in the motion records of moored ships in an actual ocean storm environment. Moreover, the basic behavior of slow oscillations is not unique to moored vessels. For instance, such behavior has been observed in tests involving vessels towed through irregular waves with a constant towing force. In such case, it has been observed that the vessel velocity exhibits slow oscillations with periods in the range of 1 to 2 minutes.
When an ocean wave is propagated toward a moored vessel, part of the wave is reflected, the remainder being transmitted on beyond the vessel The conservation of wave momentum results in a net force applied to the vessel for each wave. For regular waves the consequence is a steady drift force resulting in a static shift of the average position of the moored vessel. For irregular waves, position of the moored vessel. For irregular waves, on the other hand, a varying sequence of drift forces arises in correspondence to changes in wave height and period. Investigations leading to this paper show that the ensuing long period drift oscillation of the vessel can, for many cases, be the completely dominating influence in determining maximum mooring line tension.