Errors in the technique included resistance heat- 

 ing of the electrolyte and polarization of the 

 electrodes. The effect of polarization is shown 

 where the potential gradient near the equipotential 

 wall at a;=0 is particularly steep. 



The solutions of figures 5 through 9 for 6/a= 1/2 

 are not afSne solutions; that is, they cannot be 

 "stretched out" to describe exactly the intragravel 

 flow in porous beds of different depth-length ratios. 

 The flow nets shown, however, bear resemblance 

 to and have the same general dependence on 

 boundary-potential shape as rectangular beds of 

 any depth-length ratio. 



We have seen that for uniform permeability and 

 constant bed depth, direction and magnitude of 

 interchange depend upon configuration of the 

 streambed surface. Direction and magnitude of 

 interchange vary as well with longituduial varia- 

 tions in depth and permeability of the streambed. 



Consider the streambed section of figure 10. For 

 this section the intragravel-flow streamlines wiU 

 have a form somewhat like that shown in section 

 C. Assume that all streamlines are parallel to the 

 lower bed boundary, as in B of figure 10, and that 

 water leaves or enters the streambed by a y-di- 

 rected velocity (interchange) concentrated at the 

 upper bed boundary, y=b (see Lubyako, 1956, for 

 discussion of this assumption) . By a mass balance 

 about the lamina of depth, b, width, w, and thick- 

 ness. Ax, shown in A of figure 10, 



piwyj-li— p6Mn'i|i+ii=«yWAxp. 



(14) 



In the limit as Aa; approaches zero, the interchange, 

 i^v\v=i>, is given by 



-'=-i(*"^^- 



Combining equation (15) with Darcy's law for the 

 x-directed component of velocity 



Vz=—k 



and equation (8d) yields 



u dx 



v=i>—' 



dx 



('€)■ 



(16) 



(17) 



Equation (17) agrees with the analytical and 

 analog results for interchange dnection. For con- 

 stant bed depth; d, and permeability, k, 



"'^ a '"^ dx' 



(18) 



(15) 



For a longitudinally convex streambed surface, 

 d'yi/dx' is negative, and equation (18) implies a 

 downwelling. Conversely, equation (18) indicates 

 upwelling with a concave streambed surface. 



From equation (17) I have summarized in table 

 1 the dependence of interchange upon streambed 

 permeability and geometry, both of which may be 

 regulated to control the direction of interchange. 

 Assuming that the permeability of a streambed 

 may be increased by removing fine materials 

 (Krumbein and Monk, 1942; McNeil and Ahnell, 

 1964) or that the effective gravel-bed depth (i.e., 

 depth to which intragravel flow can occur) may 

 be increased by removing fine particles from lower 

 strata, it should be possible to create the inter- 

 change patterns shown in figures 11, 12, and 13. 

 It should also be possible to control direction and 

 amount of interchange in salmon spawning areas 

 by varying the streambed-siu-face profile (fig. 14). 



STREAMLINE COMPONENTS PARALLEL 

 TO THE BED BOUNDARIES 



ACTUAL FORM OF 

 STREAMLINES 











,/- 





LAMINA ORIENTED 

 NORMAL TO STREAMLINES 



Figure 10. — Idealized concept of intragravel flow in a 

 streambed. 



Figure 11. — Interchange induced by variation of depth 

 of the streambed. 



48e 



U.S. FISH AND WILDLIFE SERVICE 



