of 16.4 feet (5 meters) was prepared for the bordered region near the pier. 

 The wave transformation is expected to be greater within this region than it 

 is outside it where the bathymetry is more uniform. 



A wave with a period of 14 seconds and height of 6.9 feet (2.1 meters-) is 

 input that is normal to the seaward boundary. The value for H/Lq and D/Lq 

 are respectively 0.0068 and 0.01 using a mean water depth of 13.1 feet (4.0 

 meters) . These values are within the applicable region as shown by the (X) in 

 Figure 1. A time step of 1.0 second is chosen to resolve the wave in time, 

 giving 14 time steps per wavelength. The grid spacing of 16.4 feet (5 meters) 

 gives about 20 points per wavelength in space for shallow water. Equation (2) 

 indicates that a computer run of 15 wave periods requires about 9 minutes of 

 IBM 3033 computer time. The actual model run required 10 minutes and cost 

 $26. 



A plot of the wave height from various positions offshore is shown in 

 Figure 3. The measured values are from gages located along the pier, while 

 the computed values are from the model along a line adjacent to the pier. The 

 two wave heights (observed and predicted) are not directly comparable. The 

 observed wave heights are significant wave height estimates from the peak 

 energy of a spectrum, while the predicted values are from a monochromatic input. 

 This difference is minimized in this example since the observed spectrum is very 

 narrow (Fig. 4). Another difference between the modeled and the observed is 

 wave direction. The best estimate of the wave direction from pressure and 

 current sensors at the pier end is toward 238° (North being 0°), which is 14° 

 from being straight down the pier. 



This report indicates that the System 21 Mark 8 model provides a reasonable 

 reproduction of the measured field wave conditions for the case of a nearly 

 monochromatic wave spectrum. Tests representing a broad wave spectra by a 

 single height and period are less successful because the energy is spread over 

 waves that propagate at different speeds, which violate the basic assumptions 

 of the model. Thus, the model's use appears best when restricted to comparison 

 studies where test cases (different structure configurations, etc.) can be run 

 with either idealized linear or cnoidal waves, or where the basic refraction- 

 diffraction patterns are to be studied. The model cannot simulate wave break- 

 ing; care must be taken to insure that breaking-wave conditions do not occur 

 in a simulation. 



The simulation discussed in this report covered about 0.2 square kilometer 

 and cost $26 in computer time. If the same grid spacing, depths, and wave 

 periods are applicable, the costs per simulation are about $130 per square kilo- 

 meter per model run or $336 per square mile on an IBM 3033 computer. On a 

 faster computer the costs may be reduced by a factor of up to 6, although the 

 machine costs may be more. Often, the largest cost is in setting up the grids. 

 In any case, practical constraints generally will limit the economic usefulness 

 of the model to a small area and only a few runs. If a study envisions the 

 need for many runs it may be more economical and perhaps more reliable to use 

 a physical model. 



A physical model should be used if wave breaking and reformation is a major 

 concern to the effort. The numerical model appears most useful for quick 

 studies of small areas where only a few alternatives are being considered. It 

 also may be useful when an initial study (perhaps during the reconnaissance 



