On gravel‐bed roughness characterization

Abstract

The random field approach for gravel‐bed roughness characterization, which is based on the presentation of bed elevations as a three‐dimensional random field, is justified as an alternative to the characteristic particle size approach. We first show that the bed elevation distribution is close to Gaussian and then investigate gravel‐bed roughness using the second‐order structure function. The latter reveals two distinct regions: a scaling region at small spatial lags and a saturation region at large scales. The scaling exponent H (a form of Hurst exponent) appears to be isotropic and universal for both manually created “unworked” gravel beds ( H =0.5) and natural water‐worked gravel beds ( H =0.79). However, the gravel‐bed roughness, in general, is not isotropic and should be characterized by three independent characteristic scales. A simple model of gravel‐bed roughness based on the structure function parameterization is developed and compared with the characteristic particle size approach.