Skip to main content
    • Aa
    • Aa

Geometry of valley growth

  • A. P. PETROFF (a1), O. DEVAUCHELLE (a1), D. M. ABRAMS (a1), A. E. LOBKOVSKY (a1), A. KUDROLLI (a2) and D. H. ROTHMAN (a1)...

Although amphitheatre-shaped valley heads can be cut by groundwater flows emerging from springs, recent geological evidence suggests that other processes may also produce similar features, thus confounding the interpretations of such valley heads on Earth and Mars. To better understand the origin of this topographic form, we combine field observations, laboratory experiments, analysis of a high-resolution topographic map and mathematical theory to quantitatively characterize a class of physical phenomena that produce amphitheatre-shaped heads. The resulting geometric growth equation accurately predicts the shape of decimetre-wide channels in laboratory experiments, 100 m-wide valleys in Florida and Idaho, and kilometre-wide valleys on Mars. We find that, whenever the processes shaping a landscape favour the growth of sharply protruding features, channels develop amphitheatre-shaped heads with an aspect ratio of π.

Corresponding author
Email address for correspondence:
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Type Description Title
Supplementary Materials

Petroff et al. supplementary material

 PDF (990 KB)
990 KB


Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 30 *
Loading metrics...

Abstract views

Total abstract views: 268 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd September 2017. This data will be updated every 24 hours.