A METHOD FOR ESTIMATING DEPTH-LIMITED WAVE ENERGY 



by 



C. Linwood Vincent 



I. INTRODUCTION 



This report presents a method for calculating a limit on the total energy 

 of a storm sea in finite-depth water based on characteristics of irregular 

 waves. The total variance, E, in the wave field is parameterized by a wave 

 height parameter, H, defined as 



H = 4.0(E) 1/2 (1) 



The energy in the wave field is directly related to E. H should be recog- 

 nized as the estimate, based on a Rayleigh distribution, of the significant 

 wave height in deep water. H, defined in this way, is often given as an 

 approximation to the significant wave height (average of highest one-third 

 waves) in shallow water as well, although there is some evidence that the 

 significant wave height may be slightly larger than this estimate. The method 

 presented for estimating H is believed valid for wave conditions where there 

 is spread in the spectrum similar to what might be expected under storm condi- 

 tions. Estimates for nearly monochromatic swell should follow monochromatic 

 wave theory as discussed in Section 7.11 of the Shore Protection Manual (SPM) 

 (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1977) ^ 

 This report represents a major departure from the SPM methods which are based 

 on regular (monochromatic) waves. There is no clear parallel to this method 

 in the SPM. 



It is important to differentiate H from other commonly defined wave 

 parameters in shallow water. H, which will be called the depth-controlled 

 wave height (spectral) , simply parameterizes the total wave energy in a spec- 

 trum. The significant wave height, H s , is traditionally defined as the 

 average of the one-third highest waves and is approximately equal to H in 

 deep water. Hu is the breaker height and H, is the largest individual wave 

 that can exist at a given depth. It should normally be expected that, in an 

 irregular sea, H and H will be less than H^ and H^. H^ will be 

 called the depth-limited wave height (monochromatic) to differentiate it 

 from H. H^ is expected to be an estimate of the largest single wave that 

 can occur in a spectrum in water of depth d. Engineering designs that 

 require the largest single wave that can occur should use the SPM methods. 



The technical background and an evaluation of this method will be provided 

 in a forthcoming CERC report. A comparison of this method to field data is 

 described in Appendix A. 



^.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore 

 Protection Manual, 3d ed. , Vols. I, II, and III, Stock No. 008-022-00113-1, 

 U.S. Government Printing Office, Washington, D.C., 1977, 1,262 pp. 



