Institution 



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SECURITY CLASSIFICATION OF THIS PAGE 



REPORT DOCUMENTATION PAGE 



Form Approved 

 OMB No 07040188 

 Exp Oate lun 30. 1986 



la REPORT SECURITY CLASSIFICATION 

 Unclassified 



lb RESTRICTIVE MARKINGS 



2a SECURITY CLASSIFICATION AUTHORITY 



2b- DECLASSIFICATION /DOWNGRADING SCHEDULE 



3 DISTRIBUTION /AVAILABILITY OF REPORT 



Approved for public release; distribution 

 unlimited. 



4 PERFORMING ORGANIZATION REPORT NUMBER(S) 

 Technical Report CERC-87-15 



5 MONITORING ORGANIZATION REPORT NUMBER(S) 



6a NAME OF PERFORMING ORGANIZATION 

 USAEWES, Coastal Engineering 

 Research Center 



6b. OFFICE SYMBOL 

 (If applicable) 



7a. NAME OF MONITORING ORGANIZATION 



6c. ADDRESS (City, State, and ZIP Code) 

 PO Box 631 

 Vicksburg, MS 39180-0631 



7b. ADDRESS {City, State, and ZIP Code) 



8a. NAME OF FUNDING /SPONSORING 

 ORGANIZATION 

 US Army Corps of Engineers 



8b OFFICE SYMBOL 

 (If applicable) 



9 PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER 



8c. ADDRESS (Gty, State, and ZIP Code) 



Washington, DC 20314-1000 



10. SOURCE OF FUNDING NUMBERS 



324-1 



11. TITLE (Include Security Classification) 

 Analytical Solutions of the One-Line Model of Shoreline Change 



12. PERSONAL AUTHOR(S) 

 Larson, Magnus; Hanson, Hans; Kraus, Nicholas C. 



13a TYPE OF REPORT 

 Final report 



13b TIME COVERED 14. DATE OF REPORT {Year, Month, Day) 15. PAGE COUNT 



FR OM Jul 86 to Dec 86 October 1987 100 



16. SUPPLEMENTARY NOTATION 



Available from National Technical Information Service, 5285 Port Royal Road, Springfield, 



COSATI CODES 



18. SUBJECT TERMS {Continue on reverse if necessary and identify by block number) 

 Coast changes (LC) Mathematical models (LC) 



Beach erosion (LC) 



Shore-lines (LC) 



19 ABSTRACT (Continue on reverse if necessary and identify by block number) 



This report presents more than 25 closed-form solutions of the shoreline change 

 mathematical model for simulating the evolution of sandy beaches. The governing equation 

 is developed in a general form, and the assumptions and techniques used to arrive at 

 tractable closed-form solutions are described. Previous solutions are reviewed, and many 

 new solutions are derived. Solutions for beach evolution with and without the influence 

 of coastal structures are given that cover situations involving beach fill of almost 

 arbitrary initial shapes, sand mining, river discharges, groins and jetties, detached 

 breakwaters, and seawalls. Techniques for combining and extending the solutions are 

 discussed. Appendixes provide details of mathematical techniques used and complete 

 derivations of selected new solutions. Such analytical solutions can provide a simple and 

 economical means to make a quick qualitative evaluation of shoreline response under a wide 

 range of environmental and engineering conditions. 



20 DISTRIBUTION /AVAILABILITY OF ABSTRACT 

 H UNCLASSIFIED/UNLIMITED □ SAME AS RPT 



□ OTIC USERS 



22a. NAME OF RESPONSIBLE INDIVIDUAL 



21 ABSTRACT SECURITY CLASSIFICATION 



Unclassified 



22b TELEPHONE (Include Area Code) 22c OFFICE SYM80L 



|t- DD FORM 1473, 84 mar 



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83 APR edition may be used until exhausted 

 All other editions are obsolete 



SECURITY CLASSIFICATION OF THIS PAGE 



Unclassified 



