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.