Geometry of alluvial fans: Effect of discharge and sediment size

The slope of an alluvial fan increases with increasing debris size and sediment concentration in the flow, and decreases with increasing discharge. Laboratory studies suggest that the discharge which controls this slope, or dominant discharge, is that which is equalled or exceeded one quarter to one third of the time that flow occurs on the fan. In contrast, the dominant discharge in perennial alluvial rivers is equalled or exceeded only about 5 per cent of the time that flow occurs in the river. The dominant discharge on fans increases with increasing debris size, reflecting the importance of threshold stress. The slope of some natural and most laboratory alluvial fans is steepest on the flanks and gentlest along the axis. Consideration of the momentum of water debouching onto a fan at its apex suggests that the difference in slope between axis and flank should be greatest on steep fans composed of relatively non‐cohesive materials because on such fans higher discharges tend to flow down the axis, whereas lower discharges can be turned to course down the flanks. On fans with gentle slopes or composed of more cohesive material the higher discharges can also be turned toward the flanks, so on such fans the difference in slope between the axis and flank is less pronounced. Field and laboratory observations support this interpretation. Because deposition at any one time on an alluvial fan is localized, some areas aggrade while others remain at a fixed elevation. This process is treated as a Markov process with the probability of diversion from an area of active deposition into an adjacent lower area increasing as the height of the active area above the mean or ‘ideal’ surface increases. Analysis of data from laboratory and natural fans suggests that the amplitude of such surface irregularities is greater on fans composed of coarser material. The data on natural fans also suggest an increase in amplitude of the irregularities with increasing fan area.