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The logarithmic mean-velocity profile is a key experimental and theoreticalresult in wall-bounded turbulence. Similarly, here we show that the topographicsurface emerging between parallel zero-elevation boundaries presents anintermediate region with a logarithmic mean-elevation profile. We use modelsimulations, which account for growth, erosion, and smoothing processes andgive rise to complex topography with channel branching and fractal rivernetworks, as well as data from a physical landscape-evolution experiment.Dimensional and self-similarity arguments are used to corroborate this finding.Our results suggest a universality of the logarithmic scaling in boundedcomplex systems out of equilibrium, of which landscape topography andturbulence are quintessential examples.

From Turbulence to Landscapes: Universality of Logarithmic Mean Profiles in Bounded Complex Systems