Error and uncertainty in estimates of Reynolds stress using ADCP in an energetic ocean state

Abstract

The challenge of estimating the Reynolds stress in an energetic ocean environment derives from the turbulence process overlapping in frequency, or in wavenumber, with the wave process. It was surmised that they would not overlap in the combined wavenumber-frequency spectrum, due to each process having a different dispersion relationship. The turbulence process is thought to obey a linear dispersion relationship, as the turbulent flow is advected with the mean current (Taylor's frozen turbulence approximation). However, the Acoustic Doppler Current Profiler (ADCP) looks at radial wavenumbers and frequencies, and finds overlap. Another approach is to exploit the physical differences of each process, namely that the wave induced velocities are correlated over much larger distances than the turbulence induced velocities. This method was explored for current meters by Shaw and Trowbridge. Upon adapting the method for the ADCP, it is found that the resulting Reynolds stress estimates are of the correct order of magnitude, but somewhat noisy. The work of this thesis is to uncover the source of that noise, and to quantify the performance limits of estimating the Reynolds Stress when using ADCP measurements that are contaminated with strong wave-induced velocities. To that end, the space-time correlations of the error, turbulence, and wave processes are developed and then utilized to find the extent to which the environmental and internal processing parameters contribute to this error. It is found that the wave-induced velocities, even when filtered, introduce error variances which are of similar magnitude to that of the Reynolds stresses.