Laboratory alluvial fans in one dimension

When they reach a flat plain, rivers often deposit their sediment load into a cone-shaped structure called alluvial fan. We present a simplified experimental setup that reproduces, in one dimension, basic features of alluvial fans. A mixture of water and glycerol transports and deposits glass beads between two transparent panels separated by a narrow gap. As the beads, which mimic natural sediments, get deposited in this gap, they form an almost one-dimensional fan. At a moderate sediment discharge, the fan grows quasistatically and maintains its slope just above the threshold for sediment transport. The water discharge determines this critical slope. At leading order, the sediment discharge only controls the velocity at which the fan grows. A more detailed analysis reveals a slight curvature of the fan profile, which relates directly to the rate at which sediments are transported.

Figure 1

(a) DigitalGlobe satellite view (from Google Earth) and (b) field photograph of an alluvial fan in the Tian Shan Mountains, China. The sediment cone is highlighted with a white dotted line. Light colors indicate freshly deposited sediments.

Figure 2

(a) Experimental setup and definitions. Fluid and sediment flows from left to right. (b) Side photograph of an experimental fan (vertical exaggeration $\times 2$).

Figure 3

Digitized fan profiles at successive times during a single experimental run (sediment discharge $Q_s=4.6\text{g}{\min }^{-1}$, water discharge $Q_w=0.60\text{L}{\min }^{-1}$). Time starts at the beginning of the experiment. Black and gray profiles are separated by $5\text{min}$.

Figure 4

Transport law of the sediments (477-$\mu \text{m}$ glass beads in glycerol mixed with 20% of water) used to build our experimental fans. Black dots: measurements, red (gray) line: Eq. (3) fitted to the data.

Figure 5

The black dotted line correspond to the evolution of the length $L$ of an experimental fan $(Q_s=7.0\text{g}{\min }^{-1},Q_w=0.82\text{L}{\min }^{-1})$. The red (gray) line corresponds to Eq. (5) with a time shift of 15 min.

Figure 6

Predicted [red (gray) line] and observed (black points) dimensionless progradation according to the dimensionless water flux.

Figure 7

Fan profiles collected at successive stages of the same experimental run $(Q_s$ = 9.1 g ${\min }^{-1},Q_w$ = 0.54 L ${\min }^{-1})$ and rescaled with their own length. Time starts at the beginning of the experiment. Black and gray profiles are separated by $5\text{min}$.

Figure 8

Evolution of the fan slope during the experimental run described in the legend of Fig. 7. The slope is measured by fitting an affine relation to the data.

Figure 9

The last five profiles of Fig. 7 (gray dots). The red (gray) line corresponds to Eq. (20) with coefficients $S_c$ and $\epsilon$ fitted to the data. Light gray dots indicate data discarded before fitting.

Figure 10

Observed dimensionless sediment flux $\epsilon$ according to the expected values for several experiments performed with various water and sediment fluxes.