FOREWORD 



A knowledge of the energy influx along a shoreline is of consider- 

 able importance to an understanding of many beach processes and long- 

 term trends in beach responses. This study represents a step toward the 

 development of a rapid method for routine determinations of wave power 

 along a shoreline, using observed or hindcast deep-water wave character- 

 istics and high-speed computer programs for the calculation of wave 

 refraction. Specifically treated here is a computer program and pro- 

 cedure for the construction of wave rays. An example of the method is 

 presented in which wave rays are brought from deep water into the Atlantic 

 shoreline of the City of Virginia Beach, Virginia. Detailed explanations 

 of the computer programs used, instructions for their operation, and 

 sample inputs and outputs are given in appendices. A series of sugges- 

 tions is also given for improvement of the method presented. 



This report was prepared by Dr. Wyman Harrison, Associate Marine 

 Scientist, Virginia Institute of Marine Science, in pursuance of Contract 

 nA-49-055-CIV-ENG-64-5 with the Coastal Engineering Research Center, and 

 in collaboration with Mr. W.Stanley Wilson, formerly a graduate student 

 at the Institute, 



The study was supported by the Coastal Engineering Research Center 

 (formerly the Beach Erosion Board of the Corps of Engineers). Computing 

 Centers at Northwestern University, the College of William and Mary, and 

 NASA (Langley Field, Virginia) extended every cooperation. Lieutenant 

 G, Griswold, Oregon State University, first suggested to the authors the 

 use of numerical methods for the calculation of wave refraction. The 

 computer program used in this report for calculating wave refraction was 

 extensively modified from a program under development in 1963 by Lieu- 

 tenant G. Griswold and Mr. F. Nagle of the U. S. Navy Weather Research 

 Facility, Norfolk, Virginia, and Mr. E. Mehr of New York University. 

 Mr. J. Gaskin of IBM and LCDR C. Barteau of the U. S. Navy Weather 

 Research Facility aided in adapting the Griswold-Mehr program for use on 

 the 7094 computer, while Mr. J. Curran and Mr. R. Libutti of IBM, aided 

 in attempts to adapt the program to the 1620 computer. Both programs 

 were considerably revised by Wilson prior to their presentation in the 

 appendices of this study. 



The authors are indebted to Professor W. C. Krumbein of Northwestern 

 University, Consultant to the Coastal Engineering Research Center, and to 

 Mrs. Betty Benson of the Northwestern University Computing Center, for 

 making available the surface-fitting program that is used in the PRMAT 

 subprogram and SURFCE subroutine of the wave-refraction program. Pro- 

 fessor B. R. Cato of the Mathematical Department of the College of 

 William and Mary, provided helpful advice at various stages of the study. 



This report is published under authority of Public Law 166, 79th 

 Congress, approved July 31, 1945, as supplemented by Public Law 172, 

 88th Congress, approved 7 November 1963. 



