N. V. M. Odd, Wallingford, UK
The analysis by the authors of this set of high-quality laboratory experiments is overly empirical and not as complete as it could be.
The experiments simulated something like an undistorted 1 : 6 densimetric Froude scale model of conditions upstream of the Tawe fixed weir during neap tides without overtopping. As such, the time scales of the experiments are realistic.
During critical periods of low river flows, when water quality is worst, the halocline–the intermediate layer of rapidly varying salinity–is almost horizontal and not as shown in Fig. 1. In reality, the intermediate layer often expands rapidly during antecedent spring tides, when turbulent brackish surface seawater (seeded with marine algae and nutrients) intrudes landward between the fresh surface and the more saline bed layers. Therefore the initial condition at the beginning of the neap tides is not a simple step function. The initial halocline (interfacial) layer may be more than 1 m thick.29 Lowering the gate on the flood tide with a moveable weir produces more flushing.
The authors appear to have evaluated a single value of the entrainment coefficient for each long test using an entrainment velocity averaged over the whole test and the initial freshwater velocity. It would be helpful if the authors could describe more exactly how they measured the vertical mixed salt flux or transport rate tr. Was the initial freshwater velocity maintained throughout each test?
The changes in the position of the interface, illustrated in Fig. 5, show that the entrainment velocity (and vertical salt flux) decreased significantly during tests with higher initial freshwater velocities (lower Rib values). Had the authors used the initial entrainment velocities (or subdivided the test results) the resulting entrainment function would have been much closer to the results of earlier researchers and the exponent would have exceeded unity (equation (15) and Figs 14 and 15). The coefficients in equation (11) (Buch) and equation (13) (Walker and Hamill) do not appear to fit with the functions shown in Fig. 15. It seems unreasonable to quote empirical exponents to four significant figures.
The detailed measurements across the interfacial layer (halocline) would also have allowed the authors to have analysed the results in terms of vertical mixing and salt flux and compare the results with mixing length theory,30 which is more general and more readily used in multi-layer mathematical models of water quality in stratified conditions.31 It should be noted, however, that results obtained from large-scale estuarine measurements may differ significantly from those obtained in small flumes as a result of the large differences in Reynolds number.
Author's reply
The schematic diagram in Fig. 1 is intended as a general representation of the stratification in any estuary containing a barrage. The contributor is correct that the model was more representative of the situation he describes and during tests the halocline was almost horizontal.
The transport rate tr was calculated from measurements taken of the rate of erosion of the saline layer and averaged over the duration of the test. With the limitations imposed by the test configurations and durations, the initial freshwater velocity could not be maintained over the duration of the test as this would have required complex feedback control of the flow. Instead, the initial flow was maintained and the authors consider this to be more consistent with field conditions. The authors note the contributor's suggestion for analysis and acknowledge that it would produce a different exponent. Within a tidal cycle the entrainment rate varies and entrainment would be calculated over a significant time period. The initial entrainment rate would not be representative of the time-averaged value. This is the justification for the approach adopted.
When the paper, as published, was reviewed it was found that equations (11) and (13) have been incorrectly quoted, with a zero missing from each coefficient. The correct equations are
and
Measurements were taken over the full range of depths including the interfacial layer. However, within the interfacial layer, the rapidly varying refractive index has a significant impact on the accuracy of measurements taken by laser Doppler anemometry. As pointed out by the contributor, the paper presents a set of high-quality laboratory experiments and, due to the lack of confidence in the results obtained in this region, the authors did not consider these data of sufficient quality to be included in the analysis.
The contributor refers to scale effect in translating the results to full-scale applications. However, unlike pervious studies, the dimensions of the test flume permitted the study to test Reynolds numbers up to values representative of full-scale estuaries. The authors therefore feel that the results obtained have direct application to field conditions.
