Ded-friction and bottom slope, but in a general sense it supports other 

 conclusions we shall draw regarding the velocity of the tip of a bore. 



The development of a bore is usually dependent on the an-iplitude 

 oi the long wave, the presence of a reverse flow, upstream of the wave, 

 md on the influences of constrictions in the path of the wave or sudden 

 changes of bed gradient. No very sim.ple explicit statement can be made 

 to define the criterion for bore formation (cf. Stoker, 1957; Freeman & 

 Le Mehaute, 1964), although it is possible with fair accuracy to specify 

 the velocity u of propagation of a bore of height H advancing into still 

 ivater of depth d. 



The classical approach to this problem by consideration of continuity 

 and momentum (see, for example. Lamb, 1932, p. Z80; Rouse, 1938; 

 Keulegan, 1949) yields the result 



u = ,/^ r (1 + H/d)(l + H/Zd) ^ ^^^ (D-6) 



As pointed out by Keulegan (1949), this formula tends to lose physical 

 meaning as d approaches zero value, equivalent to a surge over a dry 

 bed. However, Eq. (D-6) can be rendered in the fornn 



gH" [ (l+d/H)(l + H/2d) ] ^^^ (D-7) 



from which we find that when H = 6d 



u c:^ 2 ./gH" (D-8) 



The significance of Eq. (D-8) derives from the fact that it also 

 expresses the theoretical velocity of the tip of the wave over dry ground 



D-3 



