of vegetation in terms of drag coefficients, but effects on wave heights 

 were not considered. Wayne (1975) investigated the decay of very low 

 amplitude waves, from 0.126 to 0.744 foot high (0.038 to 0.227 meter), 

 traveling short distances over grass. However, he did not establish the 

 dependence of wave period, initial wave height, and water depth, or con- 

 sider the combination of wind stress with bottom friction. 



To obtain values of bottom- friction factors, estimates of Manning's 

 roughness coefficient, n, have been made using values shown in Chow 

 (1959) for flow over flood plains. These estimated roughness coefficients 

 are conservative; i.e., they are expected to give predicted wave heights 

 somewhat greater than the wave heights which actually occur. The re- 

 duction in wind stress due to vegetation extending above the water sur- 

 face is not considered. The roughness coefficient, n, can be related 

 to the friction factor, ff, for flow over ground by combining the 

 Darcy-Weisbach and Manning equations for energy losses due to friction. 

 However, the Manning equation contains a dimensional coefficient which 

 varies depending on the dimensional units in the equation. Using a foot- 

 pound-second system of units. 



where d is in feet and g is in feet per second squared. (In a meter- 

 kilogram-second system of units, the coefficient 3.60 in equation (4) be- 

 comes 8.0.) 



The roughness coefficient, n, will vary as a function of depth due 

 to the height of the vegetation in relation to the depth of the water. 

 In addition, the friction factor, ff, has an inverse relationship to 

 the water depth, d, as shown by equation (4). Values of fr. used for 

 various kinds of ground cover are shown as curves A to D in Figure 15. 

 Curve A is for a sandy bottom (Bretschneider, 1952, 1958, 1970), where 

 ff is assumed constant. This curve was used for developing the curves 

 in Figures 1 to 12. Curve B is for coastal areas with thick stands of 

 grass. The grass will create a higji resistance at low water levels where 

 the depth of water and the height of the grass are nearly equal, but the 

 resistance will rapidly diminish as the water depth becomes greater than 

 the grass height; i.e., the water particle motion under the wave is in- 

 fluenced less by the vegetation. Curve C is for higher levels of veg- 

 etation, such as brush or low bushy trees which extend above the hei^t 

 of the grass. The friction effects will be higher for curve C than for 

 curve B because the higjier vegetation will have more influence on the 

 water particle motion for any given water depth. Curve D is for tall 

 trees which will always be higher than the depth of water. The frictional 

 resistance will be high at all water levels, and somewhat higher at low 

 water levels because of the added resistance from the ground. Curve D 

 is for a relatively close spacing of trees; e.g., a second-growth pine 

 forest which will give the highest frictional resistance. A more scat- 

 tered spacing of trees would give a lower value of f^ for a given 



25 



