Estimate of Lagrangian integral scales in shallow tidal water using high resolution GPS-tracked drifters

In estuaries and natural water channels, the estimate of velocity and dispersion coefficients is critical to the knowledge of scalar transport and mixing. This estimate is rarely available experimentally at sub-tidal time scale in shallow water channels where high frequency is required to capture its spatio-temporal variation. This study estimates Lagrangian integral scales and autocorrelation curves, which are key parameters for obtaining velocity fluctuations and dispersion coefficients, and their spatio-temporal variability from deployments of Lagrangian drifters sampled at 10 Hz for a 4-hour period. The power spectral densities of the velocities between 0.0001 and 0.8 Hz were well fitted with a slope of 5/3 predicted by Kolmogorov’s similarity hypothesis within the inertial subrange, and were similar to the Eulerian power spectral previously observed within the estuary. The result showed that large velocity fluctuations determine the magnitude of the integral time scale, TL. Overlapping of short segments improved the stability of the estimate of TL by taking advantage of the redundant data included in the autocorrelation function. The integral time scales were about 20 s and varied by up to a factor of 8. These results are essential inputs for spatial binning of velocities, Lagrangian stochastic modelling and single particle analysis of the tidal estuary.

Eddy diffusivity: A single dispersion analysis of high resolution drifters in a tidal shallow estuary

In an estuary, mixing and dispersion resulting from turbulence and small scale fluctuation has strong spatio-temporal variability which cannot be resolved in conventional hydrodynamic models while some models employs parameterizations large water bodies. This paper presents small scale diffusivity estimates from high resolution drifters sampled at 10 Hz for periods of about 4 hours to resolve turbulence and shear diffusivity within a tidal shallow estuary (depth < 3 m). Taylor's diffusion theorem forms the basis of a first order estimate for the diffusivity scale. Diffusivity varied between 0.001 – 0.02 m2/s during the flood tide experiment. The diffusivity showed strong dependence (R2 > 0.9) on the horizontal mean velocity within the channel. Enhanced diffusivity caused by shear dispersion resulting from the interaction of large scale flow with the boundary geometries was observed. Turbulence within the shallow channel showed some similarities with the boundary layer flow which include consistency with slope of 5/3 predicted by Kolmogorov's similarity hypothesis within the inertial subrange. The diffusivities scale locally by 4/3 power law following Okubo's scaling and the length scale scales as 3/2 power law of the time scale. The diffusivity scaling herein suggests that the modelling of small scale mixing within tidal shallow estuaries can be approached from classical turbulence scaling upon identifying pertinent parameters.