Flow and turbulence in a tidal channel

Date

2017-06-26

Authors

Lu, Youyu

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Abstract

An acoustic Doppler current profiler (ADCP) has been tried and found suitable for taking profiles of the time-mean three-dimensional velocity, vertical shear. Reynolds stress and turbulent kinetic energy (TKE) density in a coastal tidal channel. The velocity profiles have been used to reveal the existence of a log-layer. The data collected with the ADCP have been combined with fine- and microstructure data collected with a moored instrument (TAMI) to examine the TKE budget and turbulence characteristics in tidal flows. The ADCP was rigidly mounted to the bottom of the channel and the instrument was set to rapidly collect samples of along-beam velocities. In the derivation of the mean flow vector and the second-order turbulent moments, one must assume that the mean flow and turbulence statistics are homogeneous over the distance separating beam pairs. A comparison of the estimated mean velocity against the “error” velocity provides an explicit test for the assumption of homogeneity of the mean flow. The number of horizontal velocity estimates that pass a simple test for homogeneity increases rapidly with increasing averaging distance, exceeding 95% for distances longer than 55 beam separations. The Reynolds stress and TKE density are estimated from the variances of the along-beam velocities. Doppler noise causes a systematic bias in the estimates of the TKE density but not in the Reynolds stress. With increasing TKE density, the statistical uncertainty of the Reynolds stress estimates increases, whereas the relative uncertainty decreases. The spectra of the Reynolds stress and the TKE density are usually resolved; velocity fluctuations with periods longer than 20 minutes contribute little to the estimates. Stratification in the channel varies with the strength of the tidal flow and is weak below mid- depth. The ADCP measurements provide clear examples of secondary circulation, intense up/down- welling events, shear reversals, and transverse velocity shear. Profiles of the streamwise velocity are fitted to a logarithmic form with 1% accuracy up to a height, defined as the height of the log-layer, that varies tidally and reaches 20 m above the bottom during peak flows of 1 m s ⁻¹. The height is well predicted by 0.04u*/ω, where u * is the friction velocity and ω is the angular frequency of the dominant tidal constituent. The mean non-dimensional shear, [special characters omitted],is within 1% of unity at the 95% level of confidence inside the log-layer. Estimates of the rates of the TKE production and dissipation, eddy viscosity and diffusivity coefficients and mixing length, are derived by combining measurements with the ADCP and TAMI located at mid-depth. Near the bottom (z = 3.6 m), the production rate is 100 times larger than all other measurable terms in the TKE equation. Hence, the rate of production of TKE must be balanced by dissipation. The observed rate of production is proportional to the rate of dissipation calculated using the observed TKE density and mixing length, following the closure scheme of Mellor and Yamada (1974). This proportionality holds for the entire 3 decades of the observed variations in the rate of TKE production. At mid-depth, the eddy diffusivity of density and heat, deduced from microstructure measurements, agrees with the eddy viscosity derived from measurements with the ADCP. The scaling of the log-layer height with tidal frequency in the channel is comparable to the scaling with Coriolis parameter for the log-layer in steady planetary boundary layer. However, some results are inconsistent with those from boundary layers over horizontal homogeneous bottoms. The Reynolds stress is not constant within the log-layer, and its magnitude at 3.6 m above the bottom is 3 times smaller than the shear velocity squared [special characters omitted] derived from log-layer fitting. The peak of the non-dimensional spectrum for the Reynolds stress, when compared to measurements from atmospheric boundary layer, is shifted to higher wavenumbers by a factor of 2.5. One possible explanation for these discrepancies is the influence of horizontal inhomogeneity caused by bed forms.

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Keywords

Tidal currents, Turbulence, Oceanography

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