in each wave length, or alternately, in each frequency band. Some general trends have 

 been universally observed, however; for instance, when the sea disturbance becomes higher, 

 the waves tend to become longer. One analytical form which is often quoted, probably 

 because of its age rather than its close approximation to reality, is the Neumann spectrum 

 of the form (Cj/oj^) exp {-C 2/(0^) ■> where oj is the frequency of the incremental wave com- 

 ponent measured at a point and Cj and C2 ^re constants. 



In selecting a goal for simulation in the Model Basin facility, it was first specified 

 that a Gaussian random process be generated. Next, for lack of a generally accepted theo- 

 retical form, it was decided to use the Neumann spectrum to adjust the relative weighting of 

 power content in each frequency band. This choice is perhaps not a bad one since this 

 smooth form results in a rather broad but grossly representative power distribution versus 

 frequency and avoids extreme resonance effects which could result from a more narrow distri- 

 bution interacting with the sharply tuned ship "system." 



Obviously, it would be desirable to provide for directionality in the waves generated, 

 as this is theoretically possible because of the independent control available for each of the 

 eight wavemaking systems along the short side of the basin. However, it was felt that the 

 initial work in this area should be confined to unidirectional or long-crested sea simulation 

 in order to define and resolve the new problems anticipated with wave control using the 

 hydraulic actuator system. The resulting long-crested waves would themselves be a very 

 useful research tool, simulating rather well certain highly directional wave conditions at 

 sea, and they might be expected to produce model motions generally representative of those 

 observed at sea. In fact, one can argue that in certain cases it might be highly desirable to 

 have long-crested waves in order to investigate nonlinear effects which are quite sensitive 

 to wave direction. 



In summary, the goal of this exploratory development of wave-generation procedures 

 was to reproduce a long-crested Gaussian seaway with wave lengths distributed correspond- 

 ing to the Neumann spectrum, 



BASIC APPROACH 



A very basic way of looking at the wavemaking operation is to consider it a "system" 

 in the manner of the electrical engineer; that is, to consider as a "cause" the voltage signal 

 which controls the hydraulic servo and as an "effect" the wave height that would be mea- 

 sured with a suitable transducer in the middle of the basin. To a first approximation, this 

 system could be considered linear, based on earlier studies of regular waves which indicated 

 a roughly straight-line relationship between wave amplitude and the rate of air flow to the 

 domes. 



A basic description of a linear system is its frequency response which, in this case, 

 is a ratio of the wave height observed in the water to the sinusoidal voltage applied to the 

 actuator controls. The first such measurement with the actuators (see Figure 2) was the 

 starting point of the programming effort, 



4- 



