A second possible explanation of the nonlinearity results when the 

 "drift force" on the breakwater is considered. If one carries the hydro- 

 dynamic analysis to second order, there are terms at zero frequency 

 which yield a force on the breakwater in the direction in which the in- 

 cident waves are traveling. This force has the same effect as increas- 

 ing the initial tension in the mooring line and is proportional to wave 

 amplitude squared. Increasing the initial tension tends to increase 

 the spring constants of the mooring lines leading to larger oscillating 

 forces as well. 



(2) Alaska-Type Breakwater . Mooring-force coefficients 

 theoretically predicted and measured for the Tenakee, Alaska, breakwater 

 are shown in Figure 18. For the field data the mooring-force coefficient 

 is obtained by taking the square root of the mooring-force spectral 

 density divided by the incident wave spectral density and then dividing 

 by the weight per unit length of the breakwater. Again, as with the Oak 

 Harbor model experiments, there is good agreement, especially in predict- 

 ing the peak in the curve near B/L of 0.65. 



One important aspect of the mooring line problem which should not 

 be overlooked is a comparison between the model-scale results and the 

 field measurements. For the Alaska- type breakwater, all the measured 

 results indicate the amplitude of oscillation in mooring line force is 

 in the order of hundreds of pounds, not thousands of pounds, as was pre- 

 dicted for the Oak Harbor breakwater in the model-scale tests. 



When the mooring line tension data recorded at Tenakee are plotted 

 as a function of time as in Figure 19, one observes that there clearly 

 are oscillations associated with the incident waves. However, there are 

 also low-frequency oscillations which are of greater magnitude. A com- 

 plete explanation of the origin of these low-frequency forces has not 

 been developed. However, one possible explanation is that these forces 

 are a result of breakwater oscillation at the sway resonant frequency. 

 Since the spring constant for sway motion is very small, one would ex- 

 pect a long natural period. Theoretically predicted sway motion response 

 for the breakwater is plotted in Figure 20. Predicted natural periods 

 are 64^ 37, and 29 seconds for tidal conditions of mean lower low water 

 (MLLW) , +10 and +20 feet, respectively. By applying a high-pass filter 

 to the field data, one obtains the spectrum of force oscillation shown in 

 Figure 4. Here, a peak is at a period of about 53 seconds (tide height 

 = +7 feet) . The predicted sway natural frequency is at 45 seconds when 

 the tide height is +7 feet, which indicates that this explanation is 

 plausible. 



(3) Friday Harbor Breakwater . The predicted performance of a 

 seaward mooring line on the Friday Harbor breakwater is shown in Figure 

 21 for a tide height of +5.33 feet. The Friday Harbor mooring lines are 

 different than those at the other breakwaters. They are composed of a 

 section of chain attached to the breakwater, followed by a length of 

 nylon rope and, finally, another section of chains at the bottom. This 

 particular tidal condition was chosen because it is the condition during 

 record FH 7-8 used later for comparison. 



43 



