2. Predicted Inlet-Bay Response to Monochromatic Long Wave Forcing . 



The response of each of the inlet-bay systems (Table 2) to uniform 

 long wave forcing was evaluated using the numerical model. In this 

 analysis, a sinusoidal wave was used to force the model for several 

 cycles (generally four) until the inlet-bay system response became 

 periodic. The results will give an upper limit of wave amplification 

 and inlet velocities because the prototype will generally not reach a 

 periodic condition. 



Each inlet was modeled by using a grid system with one to three 

 channels and two to seven cross sections. The complexity of the inlet 

 determines the number of grids used to model the friction; e.g.. Pent- 

 water with a constant width and only slight changes in depth along the 

 length of the inlet, was modeled using one channel and four cross sections, 

 Little Lake, with a more irregular inlet, was modeled using three channels 

 and five cross sections. 



Pentwater, Michigan, and Toronto, Canada (Freeman, Hamblin, and 

 Murty, 1974) , are the two harbor systems on the Great Lakes with water 

 levels recorded simultaneously inside and outside the harbor to provide 

 the necessary information for calibration of the numerical model. These 

 models were calibrated by varying the value of the Manning's friction 

 factor, n, so that the model long wave amplification is a best-fit upper 

 envelope of prototype measurements. Values of n of 0.036 and 0.062 

 were found for Pentwater and Toronto, respectively (Figs. 14 and 15). 



The numerical model as used in these analyses did not explicitly 

 account for energy losses due to radiation of long waves into the sea or 

 entrance and exit losses. These losses are incorporated into the model 

 in the form of bottom friction through model calibration. Including 

 these losses in the friction term means that Manning's n calibrated for 

 Great Lakes inlets is higher than that used in open channel flow compu- 

 tations . 



In the numerical model, the magnitude of Manning's n determines the 

 amount of energy dissipated. Larger values of n will cause higher 

 amoiints of energy loss which results in less wave amplification in the 

 bay and lower inlet velocities. The influence of n on inlet-bay 

 response to long wave forcing at Pentwater is shown in Table 4. 



Table 4. Influence of Manning's n on inlet-bay 

 response at Pentwater. 



n 



{^b/^o)max 



^max> Cft/s for 

 a^ = 0.1 ft) 



0.26 

 0.36 

 0.46 



2.1 

 1.7 

 1.4 



2.8 



1.9 

 1.5 



39 



