potential, shown in the figures to be approxi- 

 mately vertical, were obtained from the analog 

 model; the intragravel flow streamlines were 

 later drawn normal to the constant potential 

 lines to obtain a grid of "curvilinear squares" 

 (Zangar, 1953, p. 17). Actually, the lines of 

 constant potential shown are the analogs of the 

 recorded lines of constant voltage, and the intra- 

 gravel flow streamlines are the analogs of electrical 

 current vectors. Figures 5, 6, 7, and 8 show the 

 flow nets corresponding to certain of the boundary 

 potential functions, <^(x), investigated. Figure 9 

 shows the effect of changed permeability on flow. 



EFFECTS OF STREAMBED CHARACTER- 

 ISTICS ON WATER INTERCHANGE 



Accompanying each of the analog solutions 

 shown in figures 5 through 9 is a small figiu-e 

 showing the function, (l>{x), investigated. Since 

 the flow potential along the open surface is 

 approximately the elevation of the porous bed 

 surface plus a constant, i.e., (t>ix)—yi{x)-\- con- 

 stunt, each of the graphs is, in effect, a longi- 

 tudinal profile of the streambed associated with 

 the function. Figure 5 shows the pattern of 

 mtragravel flow within a streambed whose surface 

 is straight. The profile of figiu-e 6 may be viewed 

 as a longitudinal convex stream section. Figure 7 

 illustrates the intragravel flow expected in the 

 streambed beneath and beyond a rapids. 



Figure 8 illustrates intragravel flow near a 

 riffle between two low-gradient stream sections. 

 This pattern of intragravel flow typifies the 

 mechanism by which respiring salmon eggs and 

 alevins are supplied with dissolved oxygen. 

 Freshly oxygenated water downweUs into the 

 streambed, passes through the streambed's in- 

 terior where oxygen is removed by salmon em- 

 bryos or alevins, and upwells back into the stream. 



The effect of placing a sheet piling in the gravel 

 bed is shown by comparing the flow net of figm-e 

 5 with that of figiu"e 9. Note that the streambed- 

 surface potential, (p(x), in figure 9 is the same as 

 that in figure 5 where, in the absence of a sheet 

 piling, there is no interchange. The sheet piling 

 directs intragravel flow to the surface upstream 

 and induces downweUing downstream of the 

 piling. The extent of interchange induced depends 

 on the depth to which the piling is driven and the 

 nearness of its bottom edge to an impermeable 

 stratum. 



Figures 5, 6, 7, and 8 show that the flow nets 

 are characterized by variable directions of inter- 

 change: upwelling, downweUing, or interchange 

 in both dhections. Furthermore, the x-directed 

 component of intragravel flow is always positive. 

 From an analysis of many similar analog solu- 

 tions and from observations in natiual streams, 

 I have found that downweUing occurs in longi- 

 tudinaUy convex stream sections, as iUustrated 

 in figiu'e 6. Similarly, upweUing takes place in 

 longitudinaUy concave stream sections.* 



Natural stream profUes usuaUy contain alter- 

 nate convex and concave reaches which cause 

 alternate regions of upweUing and downweUing 

 of stream water into and from the streambed. 

 The penetration depth of this interchange flow 

 depends on streambed geometry, e.g., the amount 

 of curvature of the bed surface and depth of the 

 streambed. In artificial spawning channels of 

 uniform depth of streambed and uniform per- 

 meability, the bed surface is often groomed to an 

 almost flat surface, and almost no potential exists 

 for mterchange. The movement of oxygen-rich 

 water into the streambed must be by mechanisms 

 other than normal water interchange, such as 

 mechanical dispersion. 



The flow nets of figures 5 through 9 show rela- 

 tive magnitude as well as direction of intragravel 

 flow. Velocity of intragravel flow varies inversely 

 with distance between lines of flow potential. 

 When the lines are closely spaced, as at point A 

 in figure 7, intragravel flow velocity is high. 

 Widely spaced lines, as at point B in figure 7, 

 show a low velocity of intragravel flow. Numerical 

 values of velocity are calculated from equation 

 (4) , through use of a value of 



\V<t>\- 



A4, 

 "As 



taken from the flow net as iUustrated in figure 7 

 (A(/) is read as "the change in 0"). The symbol s 

 is the distance variable along a streamline. The 

 streanflines indicate the direction of intragravel 

 flow. 



' A. C. Cooper (1965), in a Study of intragravel flow in salmon redds, showed 

 results of intragravel backflow, t',<0, and upwelling beneath a convex 

 streambed surface. For this geometry the small radius of curvature of the 

 streambed surface does not allow the approximation of equation (8d), and 

 the boundary condition at the streambed surface, <i:(z), must be obtained by 

 a more rigorous approach. The geometry of Cooper's model studies suggests 

 counter pressure gradients at the streambed surface and reaches of strongly 

 variable streambed depth in the direction of flow. Such conditions would 

 account for an upstream flow of intragravel water. 



INTRAGRAVEL FLOW OF WATER IN A STREAJIBED 



485 



