TY - JOUR

T1 - Predicting the roughness length of turbulent flows over landscapes with multi-scale microtopography

AU - Pelletier, Jon D.

AU - Field, Jason P.

N1 - Funding Information:
This study was funded by award #W911NF-15-1-0002 of the Army Research Office. We thank the staff of Death Valley National Park for permission to conduct a portion of the work inside the park.
Publisher Copyright:
© 2016 Author(s).

PY - 2016/5/19

Y1 - 2016/5/19

N2 - 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.

AB - 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.

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U2 - 10.5194/esurf-4-391-2016

DO - 10.5194/esurf-4-391-2016

M3 - Article

AN - SCOPUS:84971300467

SN - 2196-6311

VL - 4

SP - 391

EP - 405

JO - Earth Surface Dynamics

JF - Earth Surface Dynamics

IS - 2

ER -