Uncertainties in Estimates of Reynolds Stress and TKE Production Rate Using the ADCP Variance Method

Abstract

The use of acoustic Doppler current profilers (ADCPs) to measure turbulent parameters via the variance method involves uncertainties due to instrument noise and flow-related errors in measurement. For weak flows, the uncertainty in Reynolds stress measurements arises mainly from instrument noise and is proportional to the square of the velocity standard deviation, while the uncertainty in the corresponding estimates of the rate of production of turbulent kinetic energy (TKE) is proportional to the cube of the velocity standard deviation. For stronger flows, the principal determining parameter is the number of individual independent velocity measurements over which the variance is calculated. These results are validated by detailed analyses of two datasets from an RD Instruments 1.2-MHz Workhorse ADCP, using a ping rate of 2 Hz with ensemble averaging at 0.5 Hz, and a ping rate of 10 Hz with ensemble averaging at 1 Hz, respectively. While increasing ping rate generally reduces the effects of instrument noise, it will not alleviate the influence of flow-related noise once the sampling interval is less than the autocovariance time scale of the turbulence. Using the fast ping rate, the uncertainty in the Reynolds stress due to instrument noise is reduced by a factor of more than 3 to ?0.02 Pa; in higher energy environments there is a reduction in the uncertainty of about 30%. The observational and theoretical estimates for the reduction in the uncertainty using the fast ping rate are in good agreement.