There exist, therefore, two rigorous mathematical solutions of the 

 wave problem for water of infinite depth: that of Gerstner (rotational, 

 closed particle orbits, velocity of wave independent of height); and 

 that of Stokes-Levi-Civita (irrotational, open particle orbits, velocity 

 of wave dependent on wave height). 



The validity of the solutions discussed is limited by the condition 

 of infinite water depth. For the case of finite depth of water, in 

 which we may consider the depth to be of an order of magnitude less 

 than the wave length, the solution of the problem is much more 

 difficult. Laplace, and later Airy, found a rigorous solution of the 

 problem which is comparable to the solution of Gerstner for infinite 

 depth. The Laplace-Airy solution defines the surface as an elliptic 

 trochoid, the particle orbits as closed ellipses, the motion as rotational, 

 and the wave velocity as independent of the wave height. 



Stokes investigated this problem and arrived at a solution to a 

 third approximation; the particle orbits are open, and the motion is 

 irrotational. This solution is not, however, rigorous, and it remained 

 for Struik, using the methods of Levi-Civita, to first find a rigorous 

 solution of the problem of an irrotational wave in finite depths. 

 Struik's solution is similar to Stokes' third approximation, and shows 

 that the velocity of propagation depends on the wave height, the 

 particle orbits are open ellipses, and the motion is irrotational. 



The present status of oscillatory wave theory may be summarized, 

 then, as follows: Rigorous solutions for infuiite water depths; solutions 

 of Gerstner and of Stokes-Levi-Civita (similar to those of Rayleigh); 

 rigorous solutions for finite water depths; solutions of Laplace-Airy 

 and of Stokes-Struilv. 



As noted by Favre, experimental confu-mation of none of these 

 theoretical solutions has been obtained. Observations of wave motion 

 in the sea are very difficult to obtain with a high degree of accuracy 

 and while laboratory studies may be made with facility and high 

 accuracy, there is no confirmation that the waves studied are true 

 counterparts of ocean waves. Observations of wave phenomena in 

 nature are essential; but laboratory studies leading to the evaluation 

 of existing theories may be invaluable as a guide to field observation 

 programs and technique. 



2. PURPOSE 



It is the purpose of this study to seek in the laboratory experunental 

 confirmation of the theories outlined above, by comparison of experi- 

 mental and theoretical values of various wave characteristics. The 

 experimental data were obtained with the equipment described in 

 section 4, and are valid only for the case of uniform water depth. A 

 short summary of previous experimental work will be foimd in 

 appendix I. 



