Alluvial fans are fan-shaped deposits of water-transported material (alluvium). They typically form at the base of topographic features where there is a marked break in slope. Consequently, alluvial fans tend to be coarse-grained, especially at their mouths. At their edges, however, they can be relatively fine-grained.
A. Analytical Solution
Develop the solution for the water table elevation h(r) in an alluvial fan water table aquifer which, in plan, is a sector of a circle as shown below. The water level at the outer boundary is held constant at h0, and the recharge rate E is constant over the aquifer. Find the expression giving the maximum water level as a function of the recharge rate and aquifer parameters.
B. Numerical Solution
Verify your analytical solution with MAGNET using a set of assumed typical parameters.
Then divide the fan into three zones of decreasing K with increasing radial distance, and explain how the solution changes. Also explain why K decreases with increasing radial distance. (In other words, why do alluvial fans tend to be coarse-grained at their mouths, but relatively fine-grained at their edges.)
Photo source: https://pages.uoregon.edu/millerm/fan.html
