All the waves will then travel according to shallow water wave theory at a speed that may be 

 calculated by the formula: 



C = Vgd" 

 where 



C = the wave propagation speed 



g = the acceleration due to gravity 

 and 



d = the basin depth . 



If a rectangular basin with vertical walls is closed at both ends, a wave starting from one end 

 will travel to the opposite end and be reflected back to its starting point in a fundamental 

 period of time that may be calculated by the formula: 



2b 

 T = 



gd 



where 



T = the fundamental resonance period 



b = the length of the basin 

 and 



d = the basin depth. 



For example, if a basin is 650 feet long and 15 feet deep, the fundamental period of the 

 wave will be about 1 minute. If small waves were propagated through a narrow entrance at 

 one end of the basin at I -minute intervals, each would add energy to the wave being 

 reflected back and forth until the amplitude of that wave would become considerably larger. 

 This would be resonant surging to the fundamental period of the basin. Since most wind 

 waves and swell that penetrate harbor entrances have periods of a fraction of a minute, such 

 resonance is unlikely to occur. However, the harmonic wave periods of the basin are 1/2, 

 1/3, 1/4, 1/5— 1/n of the fundamental, and if wind waves or swell arrive at the entrance with 

 periods equaling any of those harmonics, they may induce harmonic resonant surging in the 

 basin. The wave periods of concern would therefore be computed by the formula: 



where 



The value of m would be the number of nodes in the resultant harmonic surge-wave system 

 between the two reflecting walls. Because resonant surging is more readily induced at the 



' = -vi^ 





m = 2,3,4,- 



••n . 



30 



