Predicting the roughness length of turbulent flows over landscapes

Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc 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, z 0. Here we propose a predictive formula for z 0 that uses the amplitude and slope of each wavelength of microtopogra-5 phy within a discrete-Fourier-transform-based approach. Computational fluid dynamics (CFD) modeling is used to quantify the effective z 0 value of sinusoidal microtopogra-phy as a function of the amplitude and slope. The effective z 0 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 z 0 values 10 measured in ∼ 10 5 wind velocity profiles from southwestern US playa surfaces. Our equation is capable of predicting z 0 values to 50 % accuracy, on average, across a four order-of-magnitude range.