A METHOD FOR ESTIMATING WIND-WAVE GROWTH AND DECAY IN 

 SHALLOW WATER WITH HIGH VALUES OF BOTTOM FRICTION 



Frederick E. Cornfield 



I. INTRODUCTION 



An important factor in the planning and design of works to protect 

 upland property during periods of storm surge involves the prediction of 

 the wave height and period that will prevail at and seaward of the pro- 

 tective works (i.e., levee, dike, seawall, etc.) for the selected design 

 storm. Although improvements are needed, guidelines are available for 

 prediction of the water levels in upland areas that will result from 

 storm surge; however, no guidelines are presently available for computing 

 the wave attenuation for conditions when a storm-generated wave travels a 

 distance across a shallow flooded area where the bottom characteristics in- 

 clude vegetation which causes a moderate to high frictional stress. There- 

 fore, it is necessary to estimate the heights and periods of waves which 

 have traveled across a shallow flooded area. At times the initial heights 

 and periods of the waves may increase; i.e., when the wind stress exceeds 

 the frictional stress of the ground and vegetation underlying the shallow 

 water. The initial wave heights may decay at other times when the fric- 

 tional stress exceeds the wind stress. 



This report presents a preliminary (approximate) method for estimating 

 the growth or decay of waves traveling through shallow water over areas 

 with a high frictional resistance from vegetation. The method is based 

 on previously developed equations for wave growth over areas with low 

 bottom friction given in the Shore Protection Manual (SPM) (U.S. Army, 

 Corps of Engineers, Coastal Engineering Research Center, 1975) , and an 

 equation for the decay of gravity waves over areas with a constant water 

 depth and high bottom friction. The method uses existing shallow -water 

 wave forecasting curves by adjusting fetch lengths to account for higher 

 bottom friction. Simplifying assumptions are used. The water depth is 

 assumed to have only gradual variations, and the frictional resistance is 

 treated as bottom friction. The method presented has not been verified 

 in the field and may not be applicable to other problems relating fric- 

 tional resistance to wave development. 



Only limited data are available at this time on the effects of high 

 values of bottom friction on wind waves. Friction factors are estimated 

 by comparing vegetation to similar conditions in river channels and on 

 flood plains. The effect of the vegetation on wind stress, the possible 

 effects of motion of the vegetation, and the dense vegetation effects near 

 the water surface which will damp out short -period waves much faster than 

 long-period waves are not considered. The results obtained are considered 



l \].S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, 

 Shore Protection Manual 3 2d ed., Vols. I, II, and III, Stock No. 008-022- 

 00077-1, U.S. Government Printing Office, Washington, D.C., 1975. 



