EGU2020-7031, updated on 12 Jun 2020
EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

A model for the longitudinal patterns shaped by water on erodible rocks

Matteo Bernard Bertagni and Carlo Camporeale
Matteo Bernard Bertagni and Carlo Camporeale
  • Politecnico di Torino, DIATI, Torino, Italy (

The interactions between water and rocks create an extensive variety of marvelous patterns, which span on several classes of time and space scales. In this work, we provide a mathematical model for the formation of longitudinal erosive patterns commonly found in karst and alpine environments. The model couples the hydrodynamics of a laminar flow of water (Orr-Somerfield equation) to the concentration field of the eroded-rock chemistry. Results show that an instability of the plane rock wetted by the water film leads to a longitudinal channelization responsible for the pattern formation. The spatial scales predicted by the model span over different orders of magnitude depending on the flow intensity and this may explain why similar patterns of different sizes are observed in nature (millimetric microrills, centimetric rillenkarren, decametric solution runnels).

How to cite: Bertagni, M. B. and Camporeale, C.: A model for the longitudinal patterns shaped by water on erodible rocks, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-7031,, 2020

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Presentation version 1 – uploaded on 30 Apr 2020
  • CC1: Comment on EGU2020-7031, Andrew Gunn, 04 May 2020

    Hi Matteo,

    Very interesting work, thank you. I was wondering what you expect sets the Reynolds number in the different environments? On a related note - I also see you treat the surface as smooth, whereas for real surfaces the 'roughness' will impact the flow thickness and liquid residence at the interface: could this impact your analysis?

    All the best,


    • AC1: Reply to CC1, Matteo Bertagni, 04 May 2020

      Dear Andrew,

      thank you for the questions. Regarding the first one, water may generally come from rain or snow melt.  If we talk about rain, its direct impact on rocks generate quite low Re number. However, if it has the possibility to accumulate upstream of a rock (because of runoff), then the Re may increase considerably. In this perspective, we may explain why wandkarren (quite large karren) are observed on nearly vertical walls (higher Re). Very low Reynolds number may be instead generated by dew or sea spray, which are commonly associated to microrill (small karren) formation.
      Regarding the role of roughness, it may absolutely affect the pattern formation, acting as a forcing with a specified spatial structure. I'm thinking of rain drops and the rock texture, for example. I would be interested to study this dynamics, however, at the moment, I don't really know how to deal with it analytically.

      Hope this is clear.

      Best regards