7 Gravity currents
1990 1995 2000 2005
0 10 20 30 40 50 60
Flow duration in days
Year (a)
1990 1995 2000 2005
0 0.5 1 1.5 2 2.5
Normalised flow volume
Year (b)
Figure 7.2: a) duration of gravity flows [days] and b) down shelf transport normalised by the volume of Hervey Bay. The gravity flows are tracked between Lady Elliot Island and Break Sea Spit. A gravity plume is defined to be bound by theσt=25.4 [kg/m3] isoline. This is equivalent to a depth of approx. 150 m. The duration and the down shelf transport are only counted past the 100 m depth isoline.
8 Conclusion
In this study the ocean model COHERENS has been applied to compute, amongst the usual hydrodynamic variables, the temperature and salinity distribution within Hervey Bay, Aus-tralia. A model validation and calibration has been carried out using recent in-situ field, satellite AVHRR SST data, and pan evaporation measurements. Observations and model re-sults show that the bay is in parts vertically well mixed throughout the year. The absence of longer lasting stratification is caused by the tidal regime within Hervey Bay. The tidal range can exceed 3.5 m. Due to the tidally induced bottom shear, the whole water column is con-trolled by the bottom Ekman layer most of the time. Therefore only horizontal fronts appear.
Only during a short time around neap tide, a temperature induced stratification can develop and the bottom to surface density difference can exceed 0.3 kg/m3. The dominant mechanism forcing residual circulations in the bay is provided by the Trade winds from the east, with a northern component in autumn and winter, and a southern component in spring and summer.
The wind-induced currents are in the range of 5-10 cm/s. The contribution of the tides to the residual currents is negligible. Hence, the tides are only responsible for mixing.
To quantify the impact of the residual circulations on the water exchange of Hervey Bay with the northern shelf/open ocean, the concept of flushing time and residence time was introduced.
Because both measures are defined in different frameworks (Eulerian/Lagrangian), different aspects of the water exchange could be investigated. The weak tidal residual currents lead to flushing/residence times of approx. 3 months. During SE wind conditions (Trade winds), the water exchange times were in the range of 20 days. The clockwise circulation pattern yield faster flushing times for the western part of the bay compared to the eastern part. During NE wind, the exchange time scales are comparable to SE wind, only the pattern changed. Due to the large-scale circulation cell, that connects Hervey Bay with the northern shelf (during NE wind), the central part of the bay showed the fastest response. This outflow of Hervey Bay water through the central part of the bay could also be observed in the temperature pattern of the September 2004 field trip.
Climatological data indicate that Hervey Bay is a hypersaline bay that also exhibits features of an inverse estuary, due to the high evaporation rate of approximately 2 m/year, a low pre-cipitation rate of less than 1 m/year and an on average almost absent freshwater input from the two rivers that drain into the bay. As in other inverse estuaries, the annual mean salinity increases towards the shore to form a nearly persistent salinity gradient. The region therefore acts as an effective source of salt accumulation and injection into the open ocean. The high
8 Conclusion
evaporation is leading to a loss of freshwater and increases salinity within the bay. The aver-age salinity flux into the open ocean is estimated to be about 4.0 tons/s. This study showed that this transport is mainly caused by advective transport, whereas the diffusive transport is on average three orders of magnitude smaller. Furthermore, the evaporation loss and the accumulation of salt within the bay leads to evaporation induced residual circulation of the order of 2-4 cm/s.
The numerical modelling that was carried out made it possible to understand in detail, how the actual drying trend on the east coast of Australia impacts on the hydrodynamics of Her-vey Bay. During the last two decades the drying trend has manifested itself in a reduction of precipitation by 13 % and a reduction in river discharge by 23 %. This is much higher than the long-term variability suggested and shows the impact of severe droughts during the last two decades. As a direct consequence, hypersaline/inverse conditions are more persistent but they did not increase in magnitude. Further the baroclinic residual circulation accelerated by 18 % due to the disturbance of the evaporation/precipitation ratio. The signal visible in the salinity flux shows an increase by 22 % but the annual variations are higher than the trend. Thus, longer simulation times should give more confidence. Due to the lack in boundary conditions and forcing data, the simulations could only run from 1990 onward.
Due to the inverse conditions and thus gravitational unstable conditions, gravity currents are released. These flows have a duration of approx. 30 days and are associated with a volume transport comparable to the total volume of Hervey Bay. The signature of these outflow events can be found up to depths of 280 m. A clear signal due to the reduced freshwater supply is not visible, but the model indicates a slight increase in volume transport and duration.
Despite the drying trend, two major flood events occurred in Hervey Bay 1992 and 1999. The riverine freshwater flow is restricted to an approx. 10-15 km narrow band along the western shore of the bay. The simulations yield that essentially most of Hervey Bay is unaffected by the floods. The recovery time, to an undisturbed state, follows an exponential law with a typical decay time of 22 days. This time scale is similar to a flushing time for the western bay due to SE winds. Thus, the export of the freshwater is strongly affected by the wind conditions at the time of the event.
Due to the lack of validation data for biology/chemistry, only the impact on the hydrodynam-ics could be investigated. Therefore the understanding of the influence of the drying trend on the local flora/fauna would be of great interest but is at this stage of rather speculative nature.
Although the simulation time span is with 18 years rather short and is biased by severe El Ni˜no/La Ni˜na events, the simulations demonstrate that recent climate trends impacted on physical marine conditions in subtropical regions of eastern Australia and are likely to do so in the future if current climate trends, especially drying, are to continue.
A Particle tracking schemes
A.1 Introduction
The behaviour of particles in turbulent flows has been studied for many years, ranging for me-teorology [Brickman and Smith, 2001; Cencini et al. , 2006] to ocean dynamics [North et al. , 2006; Visser, 1997, 2008]. Extensive literature exists on the treatment of Lagrangian trajec-tories, ranging from highly idealised flows to situations as complex as the unstable convective boundary layer or frontal zones. The level of understanding of these types of models has greatly increased over the years. In the same time the need to predict the transport of parti-cles, pollutants, or biological species has resulted in a rapid rise in the use of these numerical models.
The random walk simulation model enables the observation of phenomena on scales much smaller than the grid size, as well as the tracing of the movement of individual particles, thereby describing the natural processes more accurately. Furthermore, information on inte-grated properties like: residence/settling time or individual tracks are easily extracted from the simulations. Concentrations of particles can be directly calculated from the spatial posi-tions of the particles and, more importantly, when and where required. Additionally, errors due to numerical diffusion inherent in methods such as finite differences or finite elements, are avoided, particularly in areas where high concentration gradients exist, such as close to point sources or frontal zones. Although there are methods to circumvent these difficulties [Chung, 2002], their implementation is problematic in complex geometries, where it is difficult to control the potential sources of error.
The development of particle tracking methods (or random walk / random dispersion methods) started by tracking neutrally buoyant particles, i.e. water parcels [Maier-Reimer and S¨undermann, 1982; Visser, 1997]. Hunter et al. [1993] and Visser [1997] also showed that due to the high spatial variability of turbulence, the tracking algorithms need special modification to avoid numerical artefacts. In recent years, a catalogue of test cases was developed to compare the performance of tracking schemes but also to validate the models [Brickman and Smith, 2001; Deleersnijder et al. , 2006a; Spivakovskaya et al. , 2007]. Deleersnijder et al. [2006a]
extended the test catalogue to particles that have a finite sinking velocity. By this, particle tracking schemes dealing with sediment or buoyant particles could be validated against an ana-lytical solution. The random walk schemes for modelling suspended particulate matter (SPM) dynamics are quite attractive, because they give a straightforward physical interpretation of
A Particle tracking schemes
the processes and automatically account for suspension and bed load.
Because of these advantages, Lagrangian schemes have also become more common in the SPM modelling community [Charles et al. , 2008; Krestenitis et al. , 2007; Rolinski et al. , 2005].
Nevertheless most of these models used only small number of particles O(104). Nowadays with easy access to high performance computer clusters, the tracking of individual particles can be parallelised with high efficiency and therefore makes huge particle numbers feasible [Charles et al. , 2008]. This means to deal with particles in the order of >107. This is still negligible, by realising that a bucket of muddy water contains more individual particles, com-pared to the ability of state of the art Lagrangian schemes. Nonetheless increasing the number of particles leads to a better statistical description and makes the answers, a Lagrangian model can give, more reliable.