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through July 1991. Each research flow took place over an ll-day period during which the hourly releases had been specified by the researchers, Research flows were planned to provide opportunities to make mea- surements under known and controlled steady and unsteady flow conditions, The unsteady research flows were designed to test releases similar to those for power generation - low releases at night and high releases during the middle of the day, Two research flows in May 1991 were selected for velocity and dis- persion measurement because (1) these flows allowed evaluation of the difference in fluid transport during steady and unsteady releases; (2) these flows were the pair of steady and unsteady releases with the highest, and approximately equal, daily mean discharge (425 m3/s), and high flows have substantially greater capacity for sediment transport than lower flows; (3) a dense network of stage gages was available to provide detailed information on stage changes throughout the study reach during the period of unsteady flow; and (4) suspended-sediment concentrations, and therefore loss of dye through adherence to sediment, were expected to be lowest in May, High suspended- sediment concentrations typically result from runoff in tributaries, and in northeast Arizona, rainstorms that produce runoff are less likely in the late spring and early summer than at other times of the year, Description oftM Study Reach Channel geometry of the 406-kilometer study reach is variable and to a large degree controlled by bedrock type and structure (Howard and Dolan, 1981). More than 60 percent of the bed is covered by bedrock, talus blocks, and boulders (Wilson, 1986), Geometry ranges from narrow bedrock channels char- acterized by rapids and pools typically 15 m or more deep to wide, shallow, channels with large midchan- nel gravel bars, Sand is stored in the pools in thin, discon tinuous layers on a bedrock or gravel bed, Channel constrictions formed by debris deposits at the mouths of tributary streams, bedrock projections, or talus cause flow separation and eddies in all mea- sured reaches, Although eddies occur in most streams, they are a characteristic feature of the Col- orado River in Grand Canyon where the very rough and resistant bed causes flow separation in many locations (Schmidt and Graf, 1990; Schmidt, 1990), Typical eddies range in length from 150 to 500 m at moderate flow, and flow velocity in eddies is typically 20 to 40 percent of the velocity in the downstream flow of the adjacent main channel (Schmidt, 1990), Transfer of water and sediment between the main downstream flow and the eddies is of major concern because eddies are the primary depositional sites for WATER RESOURCES BULLETIN GTaf sand bars in this incised bedrock river. Also, shallow areas with low-velocity flow are formed in the eddy zones when stage in the main channel is low enough to expose the sand bars that are typical of the eddy zones, The low-velocity areas, called backwaters by fisheries biologists, may be important to the survival of native fish (Maddox et at" 1987), Study Approach Measurements were made by injecting rhodamine WT, a red fluorescent dye developed as a water tracer, into the river and collecting water samples as the dye passed selected sites downstream from the injection, Sampling was planned to begin before the arrival of the dye at a site and continue until the dye had passed the sample site, A mass of water marked by a tracer dye will move with the mean flow of the stream and mix with sur- rounding water to form a dye cloud of increasing length and decreasing concentration, Mixing and spreading in rivers are caused primarily by turbulent diffusion and velocity gradients (Fischer, 1973), A one-dimensional diffusion equation, in which flux is directly related to a concentration gradient by a diffu- sion coefficient, is commonly used to describe longitu- dinal dispersion - spreading of a mass of water in a downstream direction - in rivers (Fischer, 1973), According to that theory, the distribution of dye con- centration with time at a point downstream from the point at which the dye has become mixed throughout the width and depth of flow will be positively skewed - the mean concentration or centroid of the dye cloud will trail the peak concentration, Variance of the con- centration distribution will increase linearly with time, and peak concentration will decrease as the square root of traveltime of the peak concentration increases (Nordin and Sabol, 1974), A number of stud- ies have shown that one-dimensional theory does not adequately describe longitudinal dispersion in many rivers (Nordin and Sabol, 1974; Day, 1975; Godfrey and Frederick, 1970; Seo, 1990), Typically, concentra- tion distributions in rivers are more positively skewed and variance of the distribution increases at a greater rate than predicted by one-dimensional theory, Also, measured distributions typically have long tails not predicted by one-dimensional theory, The tails gener- ally are attributed to temporary storage in zones of slowly moving or nonconveying parts of the channel along the channel bed and banks, Much of the effort to develop models of longitudinal dispersion has focused on accounting for the "dead zones. along the channel (Bencala and Walters, 1983; Seo, 1990; Valen- tine and Wood, 1977), i ~ " 268