A SUMMARY OF THE THEORY OF OSCILLATORY WAVES 



Section 1. INTRODUCTION 



Quantitative predictions of the effect of wave action in shore-line 

 processes requires, first, statistical information on the wave height, 

 length, period, and direction, and water depth, at each locality for 

 each season; and second, a precise knowledge of the behavior of waves 

 approaching a shore line through deep water, into and through shoal- 

 ing water. This paper deals with the second phase only, presenting 

 a summary of the theoretical treatments of oscillatory wave motion 

 on a free water surface. It is limited to the type of wave encoimtered 

 in shore protection problems. Much of the theory requires experi- 

 mental verification, and mention will be made of the extent to which 

 confirmation has been obtained, without, however, quoting experi- 

 mental results. 



The derivations of equations, where not given herein, are to be 

 found in the references quoted. 



Section 2. CHARACTERISTICS OF OSCILLATORY WAVES 



All wave phenomena have some elements in common and it is im- 

 portant to establish at the outset the approximate boundaries of the 

 subject to be covered by this summary. The term oscillatory has 

 been used to emphasize the periodic character of the phenomenon 

 and to eliminate the ideas associated with the term "wave of transla- 

 tion." The waves under consideration induce a steady state of 

 oscillation which differs in many particulars from the transient state 

 characteristic of a wave of translation. Tides and seiches are also 

 periodic but are of such length in comparison with the water depth 

 as to permit simplifications in analysis which are not valid for the 

 shorter period surface waves to be considered herein. Ripples are 

 periodic and are produced by the wind but are of no consequence in 

 shore-protection problems representing an initial phase in the gener- 

 ation of wind waves. Solitary and seismic waves present an essen- 

 tially different problem and are not considered here. The waves 

 under consideration are periodic disturbances under the control of 

 gravity and inertia and of such height and period as to break on a 

 sloping shore line. 



To be more specific, the waves to be discussed are those which 

 break on the shore line, throw sand into suspension, and possibly 

 generate littoral currents. Periods are usually of the' order of 4 to 

 12 seconds along ocean shore lines but may be much greater. Heights 



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