Statistics of Ocean Wave Groups

Abstract

ABSTRACT Statistical parameters are derived that describe the occurrence probability for the number and height of consecutive waves in a group, which are large compared to the average wave height. Such wave groups can create extreme forces in mooring lines of large vessels. All of the parameters that describe the statistics of wave groups can be derived from the energy spectrum representing the sea state, if the energy spectrum is assumed to contain only a narrow band of wave frequencies. Good agreement was found between the theoretical expressions derived in this paper and actual wave data. INTRODUCTION It has been shown by Hsu and Blenkarn1 that the long period sway motion and peak mooring line force observed in a model study of a barge resulted from the combined action of a sequence of consecutive high waves in the rand Oil: wave train. Such a sequence of waves will be referred to as a wave group. Independent model tank tests conducted by Remery and Hermans2 substantiated the findings presented in Ref. 1. It is anticipated that the action of wave groups may also be important in other types of ocean engineering systems that are subjected to horizontal motions with periods much longer than the period of individual waves. Such systems could include dynamically positioned vessels. In the analysis and design of such systems it would be prudent to check whether the action of wave groups could subject the systems to motions beyond those calculated on the basis of individual waves. One can either use recorded wave groups measured in the sea, or wave groups generated in a model tank as a basis to perform such a check. There are also available electronic and numerical methods to simulate ocean waves. However, in order to make proper engineering decisions, one would need to know whether the occurrence of such wave groups is a common or rare event. More specifically, one would require a probabilistic description of the basic characteristics of wave groups in order to assess the likelihood of a system to survive. The purpose of this paper is to develop tools with which one can characterize the statistics of wave groups in terms of occurrence probabilities. No attempt is made in this paper to illustrate how such statistical tools could be used in practical engineering. It is believed that development of rational procedures to utilize such tools for specific problems can best be developed by individual users. THEORETICAL DERIVATIONS In this paper a wave group will be defined in terms of the envelopes of wave crests and troughs as shown in Fig. 1. The distance between the crest envelope and the trough envelope will be called the height envelope, whereas the distance between the crest envelope and the mean water surface will be called the amplitude envelope. The height envelope indicates the change of wave heights. Similarly, the amplitude envelope indicates the change of wave amplitude. In reality, ocean waves are not symmetrical as is implied by the term, amplitude.