with an amplification factor of 1.0, as predicted by the numerical model, 

 because the wave period is much longer than the Pentwater Helmholtz period 

 of 1.8 hours. However, the 0.65-hour wave, which reaches heights of 15 

 centimeters (0.5 foot), has a negligible effect on the harbor because it 

 is much shorter than the Helmholtz period of 1.8 hours. Waves of 1.44 

 and 1.25 hours are slightly amplified by the harbor (shown by the spectral 

 analysis in Fig. 19), but these waves are difficult to distinguish in the 

 record because of the mixing of individual wave components . 



The storm event in Figure 20 shows that a different set of modes of 

 oscillation of Lake Michigan is present. The 1.44-hour wave is the 

 highest, is amplified the most, and probably generates the highest per- 

 centage of significant reversing inlet current velocities. A 1.8-hour 

 period wave is also present and is amplified. Waves shorter than 1 hour 

 are damped by the harbor. 



An unusual water level fluctuation at Pentwater where only the 1.44- 

 hour wave is dominant in Lake Michigan, is shown in Figure 21. 



As predicted previously, the 1.8- and 1.44-period waves which are 

 the sixth and eighth longitudinal modes of oscillation of Lake Michigan, 

 cause the highest current velocities. 



Figure 22 shows the wide variation of water level fluctuations 

 occurring in three different harbors along the eastern shore of Lake 

 Michigan at the same time (Pentwater and Ludington are only 2.3 kilometers 

 (11 miles) apart) . The reasons for the differences are that the forcing 

 waves outside each location are different as a result of the node-anti- 

 node pattern of seiching in Lake Michigan (see Sec. II) and because each 

 harbor responds differently to the forcing that is present (see Sec. IV); 

 e.g., the 1.44- and 1.28-hour waves in Pentwater and Ludington are not 

 noticeable in Muskegon harbor which has a Helmholtz period of 5 hours. 



The forcing of harbors on the other Great Lakes will be completely 

 different because the system of seiching varies from lake to lake; e.g., 

 on Lake Superior, wave periods of 0.59, 0.68, 0.95, 1.14, and 1.7 hours 

 occur in Little Lake Harbor (Fig. 23). Shorter period waves may also 

 occur in Lake Superior, but are not observed in the harbor because the 

 harbor dampens waves shorter than approximately 0.4 hour. 



The 1.7-, 1.14-, and 0.95 -hour waves on Lake Superior (the 7th, 10th, 

 and 11th longitudinal modes of oscillation) were observed to cause high re- 

 versing currents and associated navigation problems at Duluth-Superior; 

 e.g., on 10 June 1973, a 1.7-hour wave with a height of approximately 

 30 centimeters (1 foot) in the harbor, in conjunction with small 0.95- 

 hour period waves, affected Duluth-Superior. Velocities as high as 200 

 centimeters per second (6.5 feet per second) were generated in Duluth 

 inlet and 140 centimeters per second (4.5 feet per second) in Superior 

 (Fig. 24) . High velocities are generated in these inlets because of the 

 large forcing waves in Lake Superior at this location which have periods 



52 



