motion is periodic in character, especially if the period of this force is the 

 same as, or is in resonance with, the natural or free oscillating period of 

 the basin (see Ch. 2, Sec. V, Wave Reflection). 



Free oscillations have periods that are dependent upon the horizontal and 

 vertical dimensions of the basin, the number of nodes of the standing wave 

 (i.e., lines where deviation of the free surface from its undisturbed value is 

 zero), and friction. The period of a true forced wave oscillation is the same 

 as the period of the causative force. Forced oscillations, however, are 

 usually generated by intermittent external forces, and the period of the 

 oscillation is determined partly by the period of the external force and 

 partly by the dimensions of the water basin and the mode of oscillation. 

 Oscillations of this type have been called forced seiches (Chrystal, 1905) to 

 distinguish them from free seiches in which the oscillations are free. 



For the simplest form of a standing one-dimensional wave in a closed 

 rectangular basin with vertical sides and uniform depth (Fig. 3-48b) , wave 

 antinodes (i.e., lines where deviation of the free surface from its 

 undisturbed value is a relative maximum or minimum) are situated at the ends 

 (longitudinal seiche) or sides (transverse seiche). The number of nodes and 

 antinodes in a basin depends on which mode or modes of oscillation are 

 present. If n = number of nodes along a given basin axis , d = basin depth , 

 and ^R ~ basin length along that axis , then T^ the natural free 

 oscillating period is given by 



2^R 

 n 'gd 



The fundamental and maximum period (T^ for n = 1) becomes 



2Jl„ 



Ti ~ (3-71) 



Vid 



Equation 3-69 is called Marian's formula (Sverdrup, Johnson, and Fleming, 

 1942). 



In an open rectangular basin of length l^^ and constant depth d , the 

 simplest form of a one-dimensional, nonresonant, standing longitudinal wave is 

 one with a node at the opening, antinode at the opposite end, and n' nodes 

 in between. (see Fig. 3-48c) . The free oscillation period T' ^' in this 

 case is 



4il 



T' = ^ (3-72) 



(1 + 2n') V^dT 



For the fundamental mode (n' =0), T'^ becomes 



T' = — 2— (3-73) 



° Vid" 



The basin's total length is occupied by one-fourth of a wavelength. 



3-98 



