Stream -function theory was therefore conducted as a part of the present study. On an 

 overall basis, the Stream-function theory provided a significantly better fit to the measured 

 water particle velocities than the other theories. The standard deviation between the 

 measured and Stream-function representations was 0.17 foot/second as compared to 

 0.24 foot/second for the theory providing the next best fit. The primary significance of this 

 phase of the study is that the wave conditions are in the shallow-water region where theories 

 other than the Stream-function would be expected to provide better comparisons with 

 measurements. Although this favorable comparison is not taken as demonstration of the 

 superiority of the Stream -function for all wave conditions, the results were very encouraging 

 and, to some extent, surprising. 



The final phase of the investigation has been the development of a computer program to 

 tabulate wave quantities that would be of value to engineers in design, and that would also 

 be valuable to persons concerned with the further development and improvement of 

 water-wave theories. During the development of the tables, it has been found that more 

 meaningful information than originally anticipated could be presented. 



In the early phases of this study, dimensional variables [i.e., water depth/ (wave period) 

 and wave height/ (wave period)] were used to characterize the wave conditions (Dean, 

 1968b). This feature wiU be evident in the description of some of the results. In the latter 

 phases of the study, it was decided to characterize the wave conditions by the following 

 dimensionless quantities: h/L^ and H/L^, where h, H and L^ represent the water depth, 

 wave height, and small-amplitude deepwater wavelength, respectively. The tables are 

 developed for 40 cases of (h/L^ , H/L^). 



The results of the research are presented in two volumes. The present report (Volume I) 

 documents the research results and describes the wave tables and their appUcation. 

 Volume II presents the wave tables that have been developed for 40 cases encompassing 

 most conditions encountered in engineering design. 



It should be noted that all of the available wave theories have not been included in the 

 comparisons described earlier. Some of the theories omitted were developed during the 

 period of this research; some have been available, but were not compared, usually because 

 they are not employed extensively for engineering purposes. 



II. STREAM FUNCTION WAVE THEORY 

 Introduction 



At an early stage of the research, the study indicated that the Stream -function theory 

 generally provided a better fit to the boundary conditions and also to available laboratory 

 measurements. The study therefore developed into an effort to explore and develop the 

 Stream-function theory for engineering application. Before presenting this work, the basis 

 for the Stream-function theory will be described in some detail in an attempt to define the 

 similarities with and differences from other theories. It should be noted that there are two 

 representations of the Stream -function theory: (1) for a given wave height, H, water 



