In order to examine the effect of wave spectral formulations on the magnitude of responses of marine vehicles and ocean structures, several wave spectra, including Pierson-Moskowitz, Bretschneider, Six-parameter, JONSWAP, etc., are selected, and computations of responses in a seaway are carried out. Responses to several hundred available wave spectra measured at various locations in the world are also included in order to provide guide lines for use of spectral formulations in design evaluations. Computations are made for four different ship types and one ocean platform, and the effect of heading to waves and speed are included in some examples.


Responses of marine vehicles and structures in a seaway, such as motions, accelerations, and wave induced forces and moments, etc., can be predicted at an early design stage by applying the modern probabilistic approach. The prediction method most commonly used considers a linear system, and the responses in a random seaway are evaluated through spectral analysis in the frequency domain.

In practice, to predict responses, an idealized spectral formulation is used as a representative of the variety of shapes of wave spectra which may be present at the desired sea severity. In reality, the shapes of wave spectra measured in the ocean vary considerably (even though the significant wave heights are the same) depending on environmental conditions such as geographic location, duration and fetch of the prevailing wind, stage of growth and decay of a storm, existence of swell, etc. References [1] and [2] show examples of the variability of spectral shape for groups of specific wave heights.

Since a marine vehicle (or ocean platform) encounters an infinite variety of wave situations, and since the magnitude of responses is significantly influenced by the shape of the wave spectra for a given sea severity, it is highly desirable to examine the limit of application of various idealized spectral formulations in design consideration.

The purpose of this paper is to present the results of a study on the effect of various wave spectral formulations on the magnitude of responses of marine vehicles and ocean structures. For this, a computer study to evaluate the responses is carried out on four ships of different types and one ocean platform using (i) several spectral formulations, and (ii) several hundred spectra measured in various locations in the world. The comparison between responses predicted in (i) and (ii) is then used to clarify which spectral formulation(s) is(are) suitable for design consideration for the various types of marine vehicles and structures considered.

The paper consists of three sections. The first section presents the spectral formulations with a brief background of each, as well as outlines the measured spectra used in the computation. The second section gives a brief discussion on prediction of responses of marine vehicles and structures in a seaway.

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