Improved Wave Kinematics From Wave Staff Arrays
Authors: Pawsey S.F.D. , Della Stritto F.J. 
Published: October 2008

ABSTRACT
A method is described for improved prediction of wave kinematics from wave staff array records. This new procedure assigns directions, as well as amplitudes and phases, to wave components at each Fourier frequency, in such a way as to fit the wave staff records best. The water particle velocities from each wave component are added vectorially with various modifications to the basic linear superposition method of the type known as "stretching."
Using storm data from Exxon's Ocean Test Structure, predicted water particle velocities are compared with measured values at a number of current meters. Evaluations are made of the importance of modifications to the superposition procedure and of the use of multiple wave staff records and directionality.

INTRODUCTION
Estimates of the magnitude of wave forces on offshore structures are based on specifying the changing elevation of the surface of the ocean. Designers must have confidence in their ability to predict, from measured wave data, wave kinematics and hence wave forces. Until the recent past, regular wave theories have normally been used to predict water particle kinematics from surface elevations measurements. However, except in rather rare circumstances, storm waves exhibit considerable irregularities. Figure 1 shows time plots of free surface elevations measured during storms. These are taken from the Ocean Test Structure (OTS) project. It is seen that both the elevations of, and the time between, successive crests and troughs, vary considerably.
If a regular wave theory is used to represent the sea, the height and period of the wave trains must be chosen from the irregular free surface data points in some way to approximate the actual observed water particle kinematics. Although this procedure forces the irregular sea to act as a regular train of waves, judicious choices of the wave height and period could result in good prediction of kinematics at a particular instant of time. Indeed, from the point of view of the designer, a regular wave theory, "tuned" to represent the observed kinematics, is likely to continue to represent the state of practice, for many structure.
In some situations, however, it may be of importance to represent the irregularity of the sea. For instance, the response of a structure that responds dynamically to waves could be greatly misrepresented by regular seas. If, as an example, the wave period was chosen exactly at a natural period of the structure, that vibration mode would start to built up dynamically with each successive wave. In reality, the importance of such a tuning would be reduced by the irregularity of the sea, with the continually changing times between wave crests.
Superposition of linear waves is an appealing method of generating irregular seas, because of both its simplicity, and its applicability to nondeterministic descriptions of kinematics. A study by Dean and Lo (3) showed that, using one wave staff to define the surface elevation record, good results could be obtained from linear superposition. This present study, also from the OTS project (1), further refines the method. The work consisted of two main thrusts.