substituting Equation 2-81 into the expression for the wavelength; there- 

 fore, 



V2 



^J = 



47.^3 



jg tanh (7rjd/4) 



, j = 1,2,---- (2-82) 



For an enclosed harbor, of approximately rectangular planform with length, 

 %, waves entering through a breakwater gap having a predominant period 

 close to one of those given by Equation 2-82 for small values of j, may 

 cause significant agitation unless some effective energy dissipation 

 mechanism is present. The addition of energy to the basin at the resonant 

 (or excitation) frequency (f^- = 1/Ty) is said to excite the basin. 



Equation 2-82 was developed by assxaming the end boundaries to be 

 vertical; however, it is still approximately valid so long as the end 

 boundaries remain highly reflective to wave motion. Sloping boundaries, 

 such as beaches, while usually effective energy dissipaters, may be signifi- 

 cantly reflective if the incident waves are extremely long. The effect of 

 sloping boundaries and their reflectivity to waves of differing character- 

 istics is given in Section 2.54, Wave Reflection from Beaches. 



Long-period resonant oscillations in large lakes and other large 

 enclosed bodies of water are termed seiches. The periods of seiches may 

 range from a few minutes up to several hours, depending upon the geometry 

 of the particular basin. In general, these basins are shallow with respect 

 to their length; hence, tanh (irjd/JJ.g) in Equation 2-82 becomes approximately 

 equal to 7rjd/Jlg and 



24 1 



T. = -r — r-w j = 1,2, (small values) . (2-83) 



] j (gd)'^ 



Equation 2-83 is termed Merian's equation. In natural basins, complex 

 geometry and variable depth will make the direct application of Equation 

 2-83 difficult; however, it may serve as a useful first approximation for 

 enclosed basins. For basins open at one end, different modes of oscilla- 

 tion exist since resonance will occur when a node is at the open end of 

 the basin and the fundamental oscillation occurs when there is one quarter 

 of a wave in the basin; hence, ilg' = L/4 for the fundamental mode and 

 T = 4£g'//gT; In general ^g' = (2- - l)L/4, and 



44' 1 

 '^i = O^ (^^ j = 1, 2, • • • • (small values) . (2-84) 



Note that higher modes occur when there are 3, 5, ...., 2^ - 1, etc., 

 quarters of a wave within the basin. 



2-116 



