fi 



ESTIMATING NEARSHORE SIGNIFICANT WAVE 

 HEIGHT FOR IRREGULAR WAVES 



by 



William N. Seelig 



I. INTRODUCTION 



The selection of design waves, as discussed in Section 7.12 of the 

 Shore Protection Manual (U.S. Army, Corps of Engineers, Coastal Engineer- 

 ing Research Center, 1977) l , is based on monochromatic wave theories. 

 The monochromatic wave theory assumption that waves have a constant 

 height and period is best applied to swell (i.e., waves generated far 

 from the point of interest) . However, wind waves and waves generated by 

 nearby storms are often irregular (i.e., height and period vary from one 

 wave to the next) , as evidenced by numerous wave records taken along the 

 coasts of the world (see Fig. 1 for two examples) . This report presents 

 design curves for the prediction of nearshore significant wave height 

 that include effects of wave irregularity, based on the procedures devel- 

 oped by Goda (1975) 2 , using known offshore (deepwater) wave conditions 

 and the nearshore bottom slope. This report does noc address factors 

 such as refraction, diffraction or nonbreaKing forms of wave energy loss. 

 A method of accounting for wave refraction for irregular waves is dis- 

 cussed in Seelig and Ahrens (in preparation, 1979) 3 . 



The analytical model requires the following assumptions: (a) the 

 deepwater unreii acted significant wave height, H<j>, and period, T, are 

 known; (b) the bottom depth is continuously decreasing from deepwater 

 shoreward; (c) the deepwater wave heights have a Rayleigh distribution; 

 (d) surf beat, wave setup, and breaking limits can be described by em- 

 pirical formulas; (e) shoaling is nonlinear; and (f) broken waves re-form 

 at lower heights. Larger waves are assumed to break in deeper water and 

 re-form, so that nearshore waves have a non-Rayleigh distribution. The 

 significant wave height nearshore cannot be used to predict other near- 

 shore height parameters, such as the mean height, because the height 

 distribution is non-Rayleigh. 



^.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. 



2 G0UA, Y., "Irregular Wave Deformation in the Surf Zone," Coastal Engi- 

 neering in Japan, Vol. 18, 1975, pp. 13-26. 



3 SEELIG, W., and AHRENS, J., "Estimating Nearshore Conditions for 

 Irregular Waves," U.S. Army, Corps of Engineers, Coastal Engineering 

 Research Center, Fort Belvoir, Va., (in preparation, 1979). 



