Because o£ the storm conditions producing the surge, it is assumed 

 that waves will always exist at the seaward edge of the initial segment 

 (i.e., H^ >> 0), and values of wind velocity, U, greater than, e.g., 

 50 miles per hour (73 feet or 22.4 meters per second) will be expected. 

 In case where H^ = 0, the methods presented here do not apply. Initial 

 wave growth would consist of very low amplitude waves with very short 

 periods. These initial waves will only be influenced by vegetation if 

 the vegetation extends above the wave surface. That case has not been 

 investigated, and cannot be treated by the method discussed in this 

 report . 



3. Adjustment- of Fetch Length . 



The adjusted fetch length of the segment is determined by comparing 

 the decay factor, Kf, for the actual bottom friction of the segment 

 (from Fig. 15) with the decay factor obtained for the friction factor 

 f ^ = 0.01 which was used for the wave predictions in Figures 1 to 12. 

 Using the method of Bretschneider (1954) (Fig. 16), the decay factor, 

 K^, is obtained by using the two factors f^:- H^ ^x/d^ and 2TTd/(gT^), 

 where Ax is the actual segment distance m feet in the direction of 

 wave motion. 



The decay factor, Kj?, was defined by Bretschneider as 



Y.f = ^ , (8) 



f/ ^i ^x / 2Trd \2 16^ Kg2 ^ ^ 



where Kg is the shoaling coefficient defined as H/Ho in Table C-1 of 

 the SPM. By noting that 



d_ ^ 2TTd 



(9) 



where L^ is the deepwater wavelength, and Kg and sinh (2'rrd/L) 

 are functions of d/L^ and therefore of 277d/(gT2), it can be shown 

 that when 2Trd/(gT^) is held constant that the right-hand side of equa- 

 tion (8) is then a function of f^ H^ hx/d^ only. 



Bretschneider (1954) used the work of Putnam and Johnson (1949) to 

 define a friction factor for an impermeable sandy bottom as f^ = 0.01. 

 The curves in Figures 1 to 12 were developed for that friction factor. 

 The wave decay is proportional to (1 - Kj?) . To compare wave decay over 

 a fetch segment with high bottom friction to wave decay over a fetch 

 segment where the bottom friction if = 0.01 (H-£, d, and U being the 

 same), a proportionality factor, a, is defined by 



28 



