Stochastic equation for the erosion of inclined topography

TL;DR

This paper introduces a stochastic model for anisotropic erosion of inclined topography, analyzing its effects with renormalization group techniques and validating predictions with seafloor data.

Contribution

It develops a stochastic equation incorporating anisotropy in erosion and provides one-loop estimates of roughness exponents validated by empirical measurements.

Findings

Predicted roughness exponents match seafloor topography data.

Anisotropy influences surface height correlations.

Renormalization group analysis reveals the role of soil inhomogeneity.

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.