Variable and conflicting shear stress estimates inside a boundary layer with sediment transport

Abstract

This paper presents a comparison between two methods for estimating shear stress in an atmospheric internal boundary layer over a beach surface under optimum conditions, using wind velocities measured synchronously at 13 heights over a 1.7 m vertical array using ultrasonic anemometry. The Reynolds decomposition technique determines at-a-point shear stresses at each measurement height, while the Law-of-the-Wall yields a single boundary layer estimate based on fitting a logarithmic velocity profile through the array data.Analysis reveals significant inconsistencies between estimates derived from the two methods, on both a whole-event basis and as time-series. Despite a near-perfect fit of the Law-of-the-Wall, the point estimates of Reynolds shear stress vary greatly between heights, calling into question the assumed presence of a constant stress layer. A comparison with simultaneously measured sediment transport finds no relationship between transport activity and the discrepancies in shear stress estimates. Results do show, however, that Reynolds shear stress measured nearer the bed exhibits slightly better correlation with sand transport rate.The findings serve as a major cautionary message to the interpretation and application of single-height measurements of Reynolds shear stress and their equivalence to Law-of-the-Wall derived estimates, and these concerns apply widely to boundary layer flows in general.

Aerodynamic Parameters Over an Eroding Bare Surface: Reconciliation of the Law of the Wall and Eddy Covariance Determinations

“…This led them to assume equality between the friction velocity obtained at this height and the surface friction velocity and thus to assume that the difference in u ∗ between LoW and EC approaches was due to a modification of κ . Our findings on the nonsensitivity of κ to wind erosion are also confirmed by the conclusion of Lee and Baas () who observed no dependence on wind erosion of their difference in u ∗ between LoW and EC approaches, meaning that the κ value was independent of the wind erosion intensity.…”

“…These small sampling frequencies may have missed a portion of the high-frequency fluctuations of w and thus underestimated the friction velocity by not accounting for the momentum transport by the smallest eddies near the surface. Unfortunately, Li et al (2010) and Lee and Baas (2016) did not present any spectra of their vertical wind velocity component or cospectra of their momentum flux to verify the adequacy of their anemometer sampling frequency. Additionally, the 2-to 5-min averaging time chosen by Li et al (2010) to derive the friction velocity from their sonic anemometer may also have been too low, missing the contribution from large eddies to the momentum transport.…”

“…This indirect evaluation of u * was justified by the use of cup anemometers measuring wind speed at low frequency (<1 Hz). Hence, most wind erosion Nowadays, the more affordable access to high-frequency anemometers (≥10 Hz) has led to a growing number of field experiments where u * is estimated directly from the correlations between the measured horizontal and vertical wind velocity fluctuations, also known as the eddy covariance (EC) approach, without requiring any assumption on the value of and on the state of the atmosphere (e.g., Li et al, 2010;Lee & Baas, 2016). This direct evaluation of u * is often considered as more reliable than the LoW approach.…”

“…The few comparisons presented in the literature on the friction velocity obtained from the above direct and indirect methods were unsuccessful (e.g., Biron et al, 2004;King et al, 2008;Li et al, 2010;Lee & Baas, 2016). They all reported differences of more than 20 to 35% on u * .…”

Distinct Thresholds for the Initiation and Cessation of Aeolian Saltation From Field Measurements

“…We assume that such conversion is possible for quasi‐instantaneous wind measurements; however, Lee and Baas () show that use of streamline‐corrected wind values for shear stress calculations may introduce errors at short time scales. Lee and Baas () further caution about uncertainties in short time scale estimates of shear stress arising from variability in turbulence structures. We also assume constant roughness height z 0 and thus neglect increasing momentum extraction by the saltation cloud with increasing saltation intensity (e.g., Sherman, ), which could further bias our calculations.…”