flow rate in) - (intragravel flow rate out) = I 

 (width of channel x length of channel) or, since 

 the width is assumed to be one unit, A W = !• 

 AL which may be expressed as first derivative, 



1 = 



dW 



dL 



(5) 



celeration or deceleration of intragravel flow. 

 A convex surface causes a faster intragravel 

 flow velocity downstream. Since, by definition, 

 the lower boundary is impermeable in this 

 model (fig. 4), water must enter the intra- 

 gravel channel, by necessity through the gravel 

 surface, to provide the additional mass flow. 



Applying this to equation (4), 



I = - k Ap cos 6 



6,6 

 "dL 



(6) 



Since kAp is positive, and fori9 < -y-, cos 6 is 

 positive, hence the sign of 1 and the direction 

 of flow depends upon the sign of-^ . Three 



cases may be considered; 



1. If the stream surface profile is a straight 



line (not necessarily horizontal), _ = and 



dL 



there is no interchange. 



6.6 



2. If the surface profile is concave,-^i^ is 



dL 

 positive, 1 is negative indicating a flow out of 



the gravel. 



3. If the surface is convex, -^2_ is negative, 



dL 



I is positive indicating a flow into the gravel. 



In other words, a curved stream surface 

 due to change in profile slope forces an ac- 



Cooper (1959) reported that under constant- 

 gradient smooth-bed surface flow conditions, 

 intragravel flow lines were generally parallel 

 to the bed with some interchange near the 

 surface. He also stated that interchange in 

 the upper 1-foot stratum was greatly in- 

 creased if large rocks were placed on top of 

 the bed, and that extensive downward inter- 

 change could be expected if a hump of gravel 

 was formed by a female salmon digging an 

 egg pocket. In either case — piled rocks or a 

 hump in the stream bed — the water surface 

 is forced to a convex profile and conditions 

 provide a force for downward interchange. 



While the curvature of the stream profile 

 induces interchange through controlling intra- 

 gravel flow velocity, a second effect is the 

 centrifugal pressure due to curved flow. It 

 may be shown, however, that usually the 

 centrifugal effect is negligible. 



Varying permeability of streambed gravel 

 is a second cause of interchange. In a stream 

 in which gravel permeability changes, although 

 the stream gradient remains constant and has 



Convex profile 



/ 



Concave profile 



Stream 



Impermeable layer 



Figure 4, --Longitudinal stream profile showing surface-induced interchange when gravel is 



underlain with impermeable layer. 



