Streamwise Dissolution Patterns Created by a Flowing Water Film

The dissolution of rocks by rainfall commonly generates streamwise parallel channels, yet the occurrence of these natural patterns remains to be understood. Here, we report the emergence in the laboratory of a streamwise dissolution pattern at the surface of an initially flat soluble material, inclined and subjected to a thin runoff water flow. Nearly parallel grooves about 1 mm wide and directed along the main slope spontaneously form. Their width and depth increase continuously with time until their crests emerge and channelize the flow. Our observations may constitute the early stage of the patterns observed in the field.

Figure 1

(a) Natural Rillenkarren on limestone (Karst plateau, Slovenia). Credit: Marko Simic. Width of picture: about 1 m. (b) Dissolution rills or Rillenkarren on gypsum (Vaucluse, France). Width of picture: about 20 cm. Credit: Pierre Thomas (https://planet-terre.ens-lyon.fr). (c)–(f) Experimental dissolution grooves. Consecutive pictures of a gypsum (plaster of Paris) block subjected to a runoff flow (inclination 39°, flow rate $Q=2.8\mathrm{L}/\min$, $U=0.84\mathrm{m}/\mathrm{s}$) for increasing times of exposure to the flow. From left to right, $t=2$, 7, 19, and 45 h. The blue lines indicate the position of water injection and the blue arrows the flow direction (b)–(f). The initial dimensions of the block are $200\times 100\times 25\mathrm{mm}$.

Figure 2

(a) Sketch of the dissolution experiment, side view. A water film of flow rate $Q$, velocity $U$, and thickness $h$ is driven by gravity and flows over a block of soluble rock of width $W=100\mathrm{mm}$, length $L=200\mathrm{mm}$, and inclined at an angle $\theta$. The block thickness $\eta (x,y,t)$ progressively decreases as it dissolves, creating a solute concentration field $c(x,y,z)$ in the flow. (b) As a result, the surface-averaged dissolved depth $⟨-\eta ⟩$ increases linearly (here during a typical experiment with $U=0.84\mathrm{m}/\mathrm{s}$, $h=380\mu \mathrm{m}$). (c) Transverse profiles $\eta (x,y,t)$ of the same experiment, measured along $y$ at a distance $x=20\mathrm{mm}$ from the water injection and plotted at various times $t$. The water level is deduced by flow conservation. Thin grooves grow over an initially flat surface and finally form channels, their crests emerging from the flow. (d) As the streamwise pattern grows, the longitudinal correlation length, which measures the maximum distance along $x$ between two correlated transverse profiles, increases until it reaches the length of the block.

Figure 3

Evolution of grooves’ morphology during five experiments. Blue circle: $Q=2.8\mathrm{L}/\min$, $\theta =39°$, $U=0.84\mathrm{m}/\mathrm{s}$, and $h=556\mu \mathrm{m}$. Green square: $Q=0.22\mathrm{L}/\min$, $\theta =39°$, $U=0.36\mathrm{m}/\mathrm{s}$, and $h=101\mu \mathrm{m}$. Orange down-pointing triangle: $Q=0.86\mathrm{L}/\min$, $\theta =39°$, $U=0.57\mathrm{m}/\mathrm{s}$, and $h=255\mu \mathrm{m}$. Red plus: $Q=1.9\mathrm{L}/\min$, $\theta =66°$, $U=0.84\mathrm{m}/\mathrm{s}$, and $h=380\mu \mathrm{m}$. Magenta star: $Q=0.93\mathrm{L}/\min$, $\theta =25°$, $U=0.51\mathrm{m}/\mathrm{s}$, and $h=305\mu \mathrm{m}$. (a) The groove typical wavelength ${\lambda }_m$ increases with time. (b) The pattern amplitude ${\sigma }_{\eta }(t)-{\sigma }_{\eta }(t=0)$ grows linearly with time. The error bars display the standard deviation along the $x$ axis. (c) Grooves’ typical wavelength rescaled by the dissolved depth ${\lambda }_m/|⟨\eta ⟩|$ versus time. (d) Pattern amplitude rescaled by the dissolved depth ${\sigma }_{\eta }/|⟨\eta ⟩|$ versus time. (e) Grooves’ wavelengths with respect to their amplitude, both rescaled by the water depth. The aspect ratio seems to be controlled by the flow depth.

Figure 4

Two scenarios of appearance of a streamwise dissolution pattern. (a) An initial perturbation of the bed is amplified because the local velocity increases with the fluid depth for a gravity driven flow. (b) The flow contains a transverse velocity variation, which is imprinted on the bed.