Extracting Reynolds Stresses from Acoustic Doppler Current Profiler Measurements in Wave-Dominated Environments

Abstract

Surface waves introduce velocity correlations that bias and often dominate Reynolds stress estimates made using the traditional variance method for acoustic Doppler current profilers (ADCPs). This analysis shows that the wave bias is the sum of a real wave stress and an error due to instrument tilt, both of which have a large uncertainty. Three alternative extensions to the variance method for calculating Reynolds stress profiles from ADCP measurements in wavy conditions are analyzed. The previously proposed variance fitting method (Variance Fit) is evaluated and two more general methods that use along- and between-beam velocity differencing with adaptive filtering (Vertical AF and Horizontal AF) are derived. The three methods are tested on datasets containing long-period monochromatic swell (Moorea, French Polynesia) and shorter-period mixed swell (Santa Barbara, California). The Variance Fit method leaves a residual wave bias in beam velocity variances, especially for intermediate waves, but gives physically reasonable Reynolds stress estimates because most of the residual wave bias cancels when the variance method is applied. The new Vertical AF method does not produce inherent wave bias in beam velocity variances, but yields comparable Reynolds stresses to the Variance Fit method. The Horizontal AF method performs poorly for all but monochromatic waves. Error remaining after one of the above methods is applied can be attributed to residual wave error, correlation of turbulence between points chosen for differencing, or correlation between waves and turbulence. A simple procedure is provided for determining the minimum bin separation that can be used.

A Comparison of Methods for Estimating Reynolds Stress from ADCP Measurements in Wavy Environments

“…The variance differencing technique, developed for acoustic Doppler velocimeters (ADVs) by Trowbridge (1998) and adapted for ADCPs by Whipple et al (2005), differenced vertically separated along-beam velocities, using linear wave theory to account for vertical decay of wave velocities with depth, before applying the variance method. Rosman et al (2008) introduced vertical (along beam) and horizontal (beam to beam) adaptive filtering (AF) to improve this method's performance for longer period waves, following a method developed for ADVs by Shaw and Trowbridge (2001). Finally, the cospectra fit (CF) method (Gerbi et al 2008;Kirincich et al 2010) estimates the stress by fitting an established semiempirical turbulence model to below-waveband cospectra.…”

“…The present work applies two methods-the vertical adaptive filtering method (Rosman et al 2008) and the cospectra fit method (Kirincich et al 2010)-to five datasets, having a range of wave and current characteristics, to determine the conditions under which successful Reynolds stress estimates can be made for each. These methods are applied to previously published ADCP velocity observations from Moorea, French Polynesia, and Santa Barbara, California (Rosman et al 2008); a pair of wave-free estuarine deployments in Elkhorn Slough, California (Nidzieko et al 2006); and the Martha's Vineyard Coastal Observatory (MVCO), Massachusetts (Kirincich et al 2010).…”

Current and turbulence measurements at the FINO1 offshore wind energy site: analysis using 5-beam ADCPs

“…Feddersen and Williams (2007) adapted the technique to reduce the wave-induced bias even further by utilising the ogive curve to check the validity of RS estimates. The techniques of Trowbridge (1998) and Shaw and Trowbridge (2001) have been recently modified by Rosman et al (2008) and Whipple et al (2006) for observations from ADCPs. They estimated the vertical attenuation of wave-induced velocities using linear wave theory before applying the variance method.…”

“…In the presence of surface gravity waves, however, contributions from the wave orbital velocities may be an order of magnitude larger than the turbulence fluctuating velocities (Trowbridge 1998;Shaw and Trowbridge 2001;Gerbi et al 2008). In such cases, even a small orientation of the instrument's head produces a large wave-induced bias in the estimated variances and covariances from ADCP measurements (Rosman et al 2008). Therefore, several methods have been suggested and applied to accurately calculate Reynolds stresses using ADCPs in the presence of surface gravity waves (Rosman et al 2008;Whipple et al 2006;Kirincich et al 2010).…”

“…In such cases, even a small orientation of the instrument's head produces a large wave-induced bias in the estimated variances and covariances from ADCP measurements (Rosman et al 2008). Therefore, several methods have been suggested and applied to accurately calculate Reynolds stresses using ADCPs in the presence of surface gravity waves (Rosman et al 2008;Whipple et al 2006;Kirincich et al 2010).…”