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Water cataracts and the “shortest-time descent” curve (Brachistochrone) as one natural phenomenon

Publication ,  Journal Article
Bejan, A
Published in: AIP Advances
February 1, 2025

This article unveils the connection between design in nature and a classic mathematics problem from 1696 to 1697: the brachistochrone. Some flow designs seem to act as obstacles to flow (cataracts, waterfalls, and roll waves), in contradiction with the natural tendency to facilitate flow (round ducts, bifurcated channels, animal speeds, and frequencies). The brachistochrone problem is to determine the curve of shortest-time descent without friction. The connection communicated in this article is that cataracts, roll waves, and the curve of shortest-time descent are about one natural phenomenon, which is predictable. This is demonstrated by comparing two ways for water to flow downhill: (i) on a stepped path (free fall over a dam, followed by accumulation in a large and nearly stagnant pool) and (ii) on a straight incline. We find that (i) is faster than (ii). In conclusion, brachistochrone-like paths are naturally occurring flow configurations, in accord with common observations of natural flow configurations that facilitate access.

Duke Scholars

Published In

AIP Advances

DOI

EISSN

2158-3226

Publication Date

February 1, 2025

Volume

15

Issue

2

Related Subject Headings

  • 51 Physical sciences
  • 40 Engineering
  • 0906 Electrical and Electronic Engineering
  • 0206 Quantum Physics
  • 0205 Optical Physics
 

Citation

APA
Chicago
ICMJE
MLA
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Bejan, A. (2025). Water cataracts and the “shortest-time descent” curve (Brachistochrone) as one natural phenomenon. AIP Advances, 15(2). https://doi.org/10.1063/5.0253849
Bejan, A. “Water cataracts and the “shortest-time descent” curve (Brachistochrone) as one natural phenomenon.” AIP Advances 15, no. 2 (February 1, 2025). https://doi.org/10.1063/5.0253849.
Bejan, A. “Water cataracts and the “shortest-time descent” curve (Brachistochrone) as one natural phenomenon.” AIP Advances, vol. 15, no. 2, Feb. 2025. Scopus, doi:10.1063/5.0253849.

Published In

AIP Advances

DOI

EISSN

2158-3226

Publication Date

February 1, 2025

Volume

15

Issue

2

Related Subject Headings

  • 51 Physical sciences
  • 40 Engineering
  • 0906 Electrical and Electronic Engineering
  • 0206 Quantum Physics
  • 0205 Optical Physics