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Stochastic equation for the erosion of inclined topography

Romualdo Pastor-Satorras·Daniel H. Rothman
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Abstract

We present a stochastic equation to model the erosion of topography with fixed inclination. The inclination causes the erosion to be anisotropic. A zero-order consequence of the anisotropy is the dependence of the prefactor of the surface height-height correlations on direction. The lowest higher-order contribution from the anisotropy is studied by applying the dynamic renormalization group. In this case, assuming an inhomogenous distribution of soil material, we find a one-loop estimate of the roughness exponents. The predicted exponents are in good agreement with new measurements made from seafloor topography.

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Romualdo Pastor-Satorras, Daniel H. Rothman. 1998-04-06. Stochastic equation for the erosion of inclined topography. https://doi.org/10.1103/physrevlett.80.4349

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