Evaluation of the Logarithmic Law of the Wall for River Flows

Abstract

The logarithmic law of the wall is commonly used to determine the shear stress applied to the river bed by the flow field. The shear stress calculation requires a velocity profile at the location of interest-data that can be obtained with a boat-mounted acoustic Doppler current profiler (ADCP). ADCP survey procedures use either a fixed-vessel (FV) or moving-vessel (MV) with each providing different spatial and temporal resolution. MV procedures require significantly less field effort but the data lack the temporal resolution of FV measurements. This fact has motivated investigators to seek MV procedures and analysis techniques that provide equivalent results to FV measurements. This study compares results of the two survey procedures for depth-averaged quantities (velocity and flow direction), mean velocity profiles, shear velocity and equivalent sand grain roughness. Mean velocity profiles are produced by time averaging for the FV measurements and spatial averaging for the MV measurements. Shear velocity and equivalent sand grain roughness are determined using simple linear regression applied to the logarithmic law of the wall. These procedures are demonstrated using data obtained during bankfull flow on the lower Roanoke River, North Carolina, USA. The results indicate comparable estimates of depth-averaged quantities from both survey procedures. Estimates of the mean velocity profiles were found to be more variable. The agreement for shear velocity and equivalent sand grain roughness was generally poor indicating that further work is necessary to produce comparable results with MV survey procedures.

Assessing Habitat Suitability for Native and Alien Freshwater Mussels in the River Waal (the Netherlands), Using Hydroacoustics and Species Sensitivity Distributions

“…In some parts of the water column, the measured flow velocity had a logarithmic relation to the water depth, which could best be assessed through semilogarithmic flow velocity profiles. These were created by using the water depth-averaged flow velocity (u) versus the natural logarithm of the vertical distance from the water surface to the measurements (z) as given by each data point measured by the ADCP [72][73][74][75][76]. Although, this logarithmic law relation is thought to only apply to the lowest 20% of the water depth, it has been previously applied throughout the water column in order to estimate flow velocity profiles [72,73,77,78].…”

“…Since the ADCP measurements were constrained to the top ~ 6 m of the total water depth, the logarithmic law was applied in order to estimate the near-bottom flow velocity. A linear regression was fitted to the logarithmic region visible in the flow velocity profiles by including at least three successive raw data points nearest to the bottom [74]. Linear regressions were acceptable if R 2 > 0.9.…”

Relating the Flow Processes and Bedforms of Steady-State and Waning Density Currents

“…This velocity data was then used to calculate the near bed shear velocity (up; Eq. 2), assuming the flow followed a standard logarithmic profile away from both the near-bed boundary layer and internal velocity maximum (Petrie and Diplas, 2015). The velocity profile was fitted over 0.01-0.02 m away from the bed in order to avoid both the near-bed viscous sublayer and the velocity maximum where the profile may deviate from the logarithmic form.…”

Método para estimar las constantes de la ley logarítmica

“…Estas regiones se evalúan por la relación ⁄ , donde es la coordenada vertical y es la profundidad o tirante del flujo. En la región cercana al fondo , la velocidad principal es descrita por la clásica "ley de pared" (Coles, 1956), que se compone de tres zonas: subcapa viscosa, amortiguamiento y logarítmica (Petrie & Diplas, 2016;Spalding, 1961). La existencia de la subcapa viscosa y la zona de amortiguamiento está en función de la rugosidad del fondo, por ejemplo, si el valor de escala de rugosidad adimensional ( , donde es la rugosidad absoluta, es la velocidad de corte y es la viscosidad cinemática), el flujo se considera con fondo hidráulicamente liso y están presentes las tres zonas.…”

“…Este modelo logarítmico se ha utilizado para caracterizar el campo de velocidad de flujos turbulentos en ríos (Ferro & Baiamonte, 2019, Instituto Mexicano de Tecnología del Agua. Open Access bajo la licencia CC BY-NC-SA 4.0 (https://creativecommons.org/licenses/by-nc-sa/4.0/) 1994; Petrie & Diplas, 2016), canales (Auel, Albayrak, & Boes, 2014;Tominaga & Nezu, 1992) y tuberías (Bailey, Vallikivi, Hultmark, & Smits, 2014;Perry, Hafez, & Chong, 2001).…”