THE SPM ENERGY FLUX METHOD FOR PREDICTING LONGSHORE TRANSPORT RATE 



by 

 Cyril Galvin and Charles R. Sohweppe 



I. INTRODUCTION 



The Shore Protection Manual (SPM) (U.S. Army, Corps of Engineers, Coastal 

 Engineering Research Center, 1977) describes procedures for estimating quanti- 

 ties important in coastal engineering design. Among the most important of 

 these is the estimation of longshore transport rate. Aside from relying 

 solely on judgment or historical data, the principal way to estimate longshore 

 transport rate is by use of the energy flux method, described in Section 4.532 

 of the SPM. Since the SPM provides design guidance rather than explanation, 

 the derivations of the energy flux equations are only briefly indicated in 

 the manual. 



This report supplements the SPM with a documented development of the energy 

 flux method as it is presented on pages 4-96 to 4-102 of the SPM. The documen- 

 tation is mainly found in the three appendixes to this report: Appendix A, 

 Derivation of the Longshore Energy Flux Factor; Appendix B, Distinction Between 

 Significant and Root-Mean-Square Wave Heights in Predicting Longshore Transport 

 Rates; and Appendix C, Field and Laboratory Data Appearing in the SPM Energy 

 Flux Discussion. The subject matter of these appendixes are the three most 

 commonly questioned aspects of the SPM presentation on the energy flux method. 

 Each appendix gives an independent explanation of one topic without necessary 

 cross-reference to other parts of the report. 



This report only describes what was done to arrive at the energy flux 

 method already published in the SPM. The assumptions necessary to arrive at 

 the formulation in the SPM are described, but not reviewed, although these 

 assumptions were closely examined by reviewers when Chapter 4 of the SPM was 

 under preparation (May 1972 to August 1973). The current issue of the SPM is 

 the third edition (1977). Section 4.532 on the energy flux method is the same 

 in all three editions, with the exception of an error on the ordinate scale of 

 Figure 4-36 which was corrected after the first (1973) printing. Galvin and 

 Vitale (1977) compared the energy flux method documented in the SPM with its 

 predecessor, TR-4, Shore Protection, Planning and Design (U.S. Army, Corps of 

 Engineers, 1966). 



II. DISCUSSION OF THE THREE APPENDIXES 



1 . The Equations (App. A) . 



The energy flux method relates longshore transport rate, Q, to wave 

 conditions by use of the longshore energy flux factor, Pj^s • Two equations 

 are needed: an equation that converts wave conditions into Piq, and an 

 equation that predicts Q from P^g. In the SPM, four theoretically equiva- 

 lent equations for longshore energy flux, P^, are developed from small- 

 amplitude, linear theory. From these four equations, four design equations 

 for the longshore energy flux factor in the surf zone, P^g, are derived. 

 Although each equation for Pj, is equivalent to any of the three other 

 equations for P^^ , no two of the four P^g equations are exactly equivalent 

 because each Pj^g equation was derived from a different P^ equation using 

 a different set of approximations. 



