Turbulent Mixing and Sediment Processes in Peri-Urban Estuaries in South-East Queensland (Australia)

Abstract

An estuary is formed at the mouth of a river where the tides meet a freshwater flow and it may be classified as a function of the salinity distribution and density stratification. An overview of the broad characteristics of the estuaries of South-East Queensland (Australia) is presented herein, where the small peri-urban estuaries may provide an useful indicator of potential changes which might occur in larger systems with growing urbanisation. Small peri-urban estuaries exhibit many key hydrological features and associated ecosystem types of larger estuaries, albeit at smaller scales, often with a greater extent of urban development as a proportion of catchment area. We explore the potential for some smaller peri-urban estuaries to be used as ‘natural laboratories’ to gain some much needed information on the estuarine processes, although any dynamic similarity is presently limited by a critical absence of in-depth physical investigations in larger estuarine systems. The absence of detailed turbulence and sedimentary data hampers the understanding and modelling of the estuarine zones. The interactions between the various stakeholders are likely to define the vision for the future of South-East Queensland’s peri-urban estuaries. This will require a solid understanding of the bio-physical function and capacity of the peri-urban estuaries. Based upon the current knowledge gap, it is recommended that an adaptive trial and error approach be adopted for their future investigation and management strategies.

Appendices

Appendices

Appendix I: Kolmogorov and Batchelor Scales

Motions in a turbulent flow exist over a broad range of length and time scales (Roberts and Webster 2002). The length scales are linked to the motion of fluctuating eddies in turbulent flows. The largest scales are bounded by the geometric dimensions of the flow, for instance the depth and width of the channel. The large scales are referred to as the integral length and time scales. Observations indicate that eddies lose most kinetic energy after one or two overturns. The rate of energy transferred from the largest eddies is proportional to their energy times their rotational frequency. The kinetic energy is proportional to the velocity squared, in this case the fluctuating velocity v, that is ascribed by the velocity standard deviation. The rotational frequency is proportional to the standard deviation of the velocity divided by the integral length scale. Thus, the rate of dissipation ε is of the order:

$$ \upvarepsilon \sim {{{{{\mathrm{ v}}^3}}} \left/ {\mathrm{ l}} \right.} $$

where l is the integral length scale. The rate of dissipation is independent of the viscosity of the fluid and only depends on the large-scale motion. In contrast, the scale at which the dissipation occurs is strongly dependent on the fluid viscosity. These arguments allow an estimate of this dissipation scale, known as the Kolmogorov microscale η, by combining the dissipation rate and kinematic viscosity ν based upon dimensional considerations:

$$ \upeta \sim {{\left( {{{{{\upnu^3}}} \left/ {\upvarepsilon} \right.}} \right)}^{1/4 }} $$

Similarly, the time and velocity scales of the smallest eddies may be derived:

$$ \uptau \sim {{\left( {{\upnu \left/ {\upvarepsilon} \right.}} \right)}^{1/2 }} $$

$$ \mathrm{ u}\sim {{\left( {\upnu\upvarepsilon} \right)}^{1/4 }} $$

An analogous length scale may be introduced for the range over which molecular diffusion acts on a scalar quantity. This length scale is referred to as the Batchelor scale L_B and it is proportional to the square root of the ratio of the molecular diffusivity D_m to the strain rate γ of the smallest velocity scales:

$$ {{\mathrm{ L}}_{\mathrm{ B}}}\sim {{\left( {{{{{{\mathrm{ D}}_{\mathrm{ m}}}}} \left/ {\upgamma} \right.}} \right)}^{1/2 }} $$

The strain rate γ of the smallest scales is proportional to the ratio of Kolmogorov velocity to length scales:

$$ \upgamma \sim {{\mathrm{ u}} \left/ {{\upeta \sim }} \right.}{{{{\upvarepsilon^{1/2 }}}} \left/ {\upnu} \right.} $$

Thus, the Batchelor length scale L_B can be recast into a form that includes both the molecular diffusivity of the scalar and kinematic viscosity of the fluid:

$$ {{\mathrm{ L}}_{\mathrm{ B}}}\sim {{\left( {{{{{v^2}{{\mathrm{ D}}_{\mathrm{ m}}}^2}} \left/ {\upvarepsilon} \right.}} \right)}^{1/4 }} $$

A further dimensionless number is the Schmidt number Sc defined as the square of the ratio of Kolmogorov to Batchelor length scales:

$$ \mathrm{ Sc}={{{\upeta \left/ {\mathrm{ L}} \right.}}_{\mathrm{ B}}}\approx {\upnu \left/ {{{{\mathrm{ D}}_{\mathrm{ m}}}}} \right.} $$

In the estuarine zone of Eprapah Creek, a typical mean velocity is 0.2 m/s with a fluctuating velocity v about 30 % of the mean, while an integral length scale is roughly half the channel depth, i.e. l ≈ 1 m. Water at 20 Celsius has a kinematic viscosity of 1 × 10⁻⁶ m²/s. Therefore, the Kolmogorov length and time scales are about 0.2 mm and 0.07 s respectively. Assuming a diffusivity D_m ≈ 1 × 10⁻⁹ m²/s for a typical chemical dye tracer, the Batchelor scale is 0.009 mm, or 32 times smaller than the Kolmogorov microscale. Thus, one would expect a much finer structure of the concentration field than the velocity field. Corresponding values for the Brisbane River are v = 0.3 m/s and l = 5 m yielding Kolmogorov length and time scales of 0.12 mm and 0.014 s, respectively. The relatively small difference in terms of scales between the two estuaries is because the increase in Kolmogorov length and time scales caused by the larger channel depth is countered by the reducing effect of the increase in mean velocity.

Appendix II: Pollution of Brisbane River and Eprapah Creek: 2001 Court Case

R v Hobson, Moore & Universal Abrasives Pty Ltd (2001) District Court Queensland, Forno DCJ, 15 June 2001, 1606/01.

R v Moore, 1 Qd R 205 (QCA, 2001).

R. v Moore – [2003] 1 Qd R 205, Court of Appeal, Williams JA, Jones J, Douglas J [2001] QCA 431 [C.A. 162/2001] 5, 12 October 2001

Queensland Court decision (2000) R. v Hobson & Moore & Universal Abrasives Pty Ltd.

In EPA v Universal Abrasives Pty Ltd and Moore and Hobson (Brisbane District Court, 2001), a company and two directors were charged with offences under the environmental protection (EP) Act in relation to the disposal of spent abrasive blasting product from a ship cleaning business in Brisbane. On 28 September 1998, the company released liquid waste containing high concentrations of heavy metals including lead, zinc, copper, arsenic, chromium, cadmium, selenium and biocide tributyltin (TBT) to a stormwater drain connected to the Brisbane River at Bulimba. The discharge was analysed and found to contain 2,700,000 μg/L TBT: that is, more than a million times the ANZECC limit of 2 μg/L. The company had also stored abrasive blasting material adjacent to the stormwater drain in a manner contravening its licence conditions. In addition, the same abrasive blasting material was stored in a manner that had the potential to cause serious environmental harm to a mangrove estuary at Eprapah Creek, Thornlands. The company failed to carry out environmental protection orders to clean up the affected sites.

The company and directors pleaded not guilty to causing serious environmental harm and to other offences, but were found guilty by a jury. That was the company and directors; second conviction under the EP Act, and the trial judge found that they showed no remorse. The company was fined $375,000. One director was given a suspended sentence of 9 months imprisonment (suspended for 3 years from sentences totalling 3 years to be served concurrently) and was fined $50,000. The other director was sentenced to 18 months actual imprisonment (based on sentences totalling 7.5 years to be served concurrently) and fined $100,000. In EPA v Moore [2001] QCA 431, the Queensland Court of Appeal rejected an appeal against one of the sentences.