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From turbulence to landscapes: Logarithmic mean profiles in bounded complex systems
Milad Hooshyar1, Sara Bonetti2, Arvind Singh3
1Princeton Environmental Institute and Princeton Institute for International and Regional Studies, Princeton University, Princeton, New Jersey 08544, USA.
Physical Review. E
|October 20, 2020
Summary
Landscape topography exhibits a logarithmic mean-elevation profile, similar to fluid dynamics. This finding, observed across various complex systems, highlights robust self-similar scaling in natural and simulated networks.
Area of Science:
- Geomorphology
- Complex Systems Science
- Fluid Dynamics
Background:
- Wall-bounded turbulence exhibits a logarithmic mean-velocity profile.
- Understanding landscape topography scaling is crucial for geomorphological studies.
Purpose of the Study:
- To investigate the presence of logarithmic profiles in landscape topography.
- To explore the universality of logarithmic profiles across different complex systems.
Main Methods:
- Analysis of model simulations of complex topographies (channel branching, fractal river networks).
- Controlled laboratory experiments on landscape formation.
- Examination of natural landscapes.
- Testing minimalist network models (optimal channel networks, directed percolation).
- Application of dimensional and self-similarity arguments.
Main Results:
- Identification of an intermediate region with a logarithmic mean-elevation profile in landscape topography.
- Logarithmic profiles were observed in simulated, experimental, and natural complex landscapes.
- Self-similar scaling emerged as a robust outcome in diverse systems.
Conclusions:
- Landscape topography shares a fundamental scaling property with wall-bounded turbulence.
- Logarithmic profiles and self-similar scaling are emergent properties of spatially bounded complex systems.
- Length-scale independence is a key factor driving these universal scaling behaviors.
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