Articles | Volume 4, issue 2
Research article
19 May 2016
Research article |  | 19 May 2016

Predicting the roughness length of turbulent flows over landscapes with multi-scale microtopography

Jon D. Pelletier and Jason P. Field

Abstract. The fully rough form of the law of the wall is commonly used to quantify velocity profiles and associated bed shear stresses in fluvial, aeolian, and coastal environments. A key parameter in this law is the roughness length, z0. Here we propose a predictive formula for z0 that uses the amplitude and slope of each wavelength of microtopography within a discrete-Fourier-transform-based approach. Computational fluid dynamics (CFD) modeling is used to quantify the effective z0 value of sinusoidal microtopography as a function of the amplitude and slope. The effective z0 value of landscapes with multi-scale roughness is then given by the sum of contributions from each Fourier mode of the microtopography. Predictions of the equation are tested against z0 values measured in  ∼ 105 wind-velocity profiles from southwestern US playa surfaces. Our equation is capable of predicting z0 values to 50 % accuracy, on average, across a 4 order of magnitude range. We also use our results to provide an alternative formula that, while somewhat less accurate than the one obtained from a full multi-scale analysis, has an advantage of being simpler and easier to apply.

Short summary
The law of the wall is one of the fundamental equations at the boundary of atmospheric sciences and aeolian geomorphology. In this paper, we quantify the relationship between the key parameter of the law of the wall, i.e., the roughness length, and measures of microtopography. We propose a method for predicting the roughness length that works for landscapes with microtopography over a wide range of spatial scales. The method is tested against approximately 60 000 measurements of roughness length.