Width convergence in tide-dominated estuaries: the case of the Alligator Rivers, Northern Australia. part of Vignettes:Vignette Collection
The Alligator Rivers region is situated in the southeast corner of Van Diemen Gulf, northern Australia (Figure 1). It contains some excellent examples of tide-dominated estuaries (Figure 2). An immediately obvious feature of these estuaries is their strong upstream decrease in channel width (Figure 2). This morphology, which is often described as a converging or funnel shaped width profile, is typical of tide-dominated estuaries (Dalrymple and Choi, 2007). In this vignette we will consider some ideas about the form of tidal channel width convergence, and its causes. Firstly however, it is useful to review some background about estuarine geomorphology. Many different definitions of the term estuary have been proposed (Dalrymple et al., 1992; Elliott and McLusky, 2002). Here we will assume that estuaries are semi-enclosed coastal water bodies, which form where rivers flow into the sea, and which receive sediment from both marine and fluvial sources. Estuaries are often classified as being either tide-dominated or wave-dominated. Theoretically, a tide-dominated estuary is one in which tidal currents are the most important driver of sediment transport in the estuary mouth (Dalrymple et al., 1992; Boyd et al., 2006). Wave-dominated estuaries can be similarly defined. Importantly, the dominance of waves or tides in an estuary is strongly related to its morphology and facies distribution. Indeed, individual estuaries are most often classified visually as either wave or tide-dominated (rather than by the measurement of process), by comparing their morphology and facies distribution to idealized wave and tide-dominated models (Dalrymple et al., 1992; Harris et al., 2002; Boyd et al., 2006). This approach was used to classify the majority of estuaries in Australia (Harris et al., 2002), and in each case the results were compared with independent estimates of the wave and tidal power at the estuary mouth. Estuaries classified as tide-dominated usually had a higher ratio of tide to wave power than did estuaries classified as wave-dominated (Harris et al., 2002), supporting the proposed relationships between process and morphology. In sum, there are strong general relationships between morphologies and dominant processes in estuaries. What are the typical morphological characteristics of tide-dominated estuaries? Although a range of different morphologies have been identified (Dalrymple and Choi, 2007), perhaps the most visually obvious is the upstream decrease in channel width. This can be seen to occur in the West, South, and East Alligator Rivers (Figure 2). In the literature, it has been commonly reported that the decrease in width occurs exponentially with distance upstream (e.g. Wright et al., 1973; Chappell and Woodroffe, 1994; Savenije, 2005). Mathematically then: Width ~ W*exp(-x/L) where W and L are fitting parameters, and x is the distance upstream. How well does the exponential relationship apply to the Alligator Rivers? Figure 3 demonstrates it is indeed a good description of the Alligator river width profiles. Given this, the exponential fit provides some convenient statistics with which to summarise the estuarine width profile. The parameter W will be approximately equal to the estuary mouth width. The parameter L describes the rate of width convergence, and can be understood as follows: Suppose that you were in a boat at some point in the estuary at which you measured the channel width. Then L approximates the distance that you would have to travel upstream for the channel width to reduce by a factor of e (~=2.718) relative to the first measurement. According to the exponential model, this distance does not depend on where in the estuary you begin. In the West, South and East Alligator Rivers, L is approximately 11, 12.5 and 10 km respectively. It is interesting that despite the large differences in the mouth size of these systems, their value of L is quite similar. Studies of other estuaries in nearby parts of Northern Australia have been conducted by Davies and Woodroffe (In Press), who found that L is typically in the range 5-30km, and does not seem related to the mouth size of the estuary (Figure 4). This result implies a strong change in estuary shape with mouth width: Estuaries with a larger mouth width tend to be more strongly funnel-shaped than those with a smaller mouth. This is illustrated visually in Figure 4, which depicts three idealised channels with similar values of L, but different mouth widths. Notice how channel 1 is most strongly funnel-shaped, with channels 2 and 3 begin progressively less so. Why do tide-dominated estuaries tend to develop an approximately exponential width profile? A key point is that the tidal discharge at a given cross-section will depend on the tidal prism upstream of it. Thus the tidal discharge will increase as one moves downstream. In order to accommodate this increasing discharge, the estuary must exhibit a downstream increase in at least one of the following: cross-sectionally averaged velocity, depth, or width. It appears that often in nature, width increases accommodate most of the increase in discharge. Mathematical arguments based on these observations, and further simplifying assumptions, suggest that estuaries with a constant tidal range and cross-sectionally averaged velocity amplitude should exhibit an exponential width profile (e.g. Chappell and Woodroffe, 1994; Savenije, 2005). While the specific assumptions of these theories differ, any theory which assumes that estuaries adapt morphologically to meet certain constraints on their 1D tidal hydrodynamics (described in terms of velocities and water levels) will predict that L is independent of the estuary mouth width (Davies and Woodroffe, In Press). Natural estuaries will of course not perfectly satisfy the strong assumptions underlying these theoretical arguments. Further work is required to fully understand the co-evolution of morphology, sedimentology and hydrodynamics in tide-dominated estuaries.
Flow in a microtidal channel during within-bank and over-bank tides: Yalimbah Creek, South Eastern Australia. part of Vignettes:Vignette Collection
The study of tidal hydrodynamics plays an important role in geomorphic studies of tidal channels. While the hydrodynamic properties of the landform are largely controlled by its morphology, these flows also drive sediment transport in the creek and its intertidal flats. They thus have a major influence on the evolution of the landform. This vignette will examine a velocity time series from a tidal channel, and consider the extent to which a simple model, based on the conservation of water mass, can explain the observations. Yalimbah Creek is a microtidal channel (tidal range usually < 2 m), situated in the north western corner of Port Stephens, a large natural harbour in South Eastern Australia (Figure 1a). The channel is largely sheltered from wave processes, and its small catchment has no inflowing river channel. For most of its length, the channel meanders through a narrow valley filled with intertidal marsh (Figures 1b, 2b,2c), the elevation of which gradually decreases downstream. At its most downstream end, the channel flows into an unvegetated intertidal cove (Number One cove, Figure 1b, 2a), where it gradually shallows until it is no longer clearly distinct from the rest of the cove. The channel is formed largely in unconsolidated muddy sediments, consisting of organic rich silt and clay, with some fine and very fine sand. In many places it is also partly bound by bedrock. Vegetated intertidal flats are known to exert a strong influence on tidal channel hydrodynamics (e.g. Wolanski et al., 1980; Lessa and Masselink, 1995). As the tide overtops the channel banks, the flats are flooded, and the volume of water stored in the channel/flats system increases rapidly with tidal stage. The flow velocities on the flats tend to be much lower than in the channel, because the former have smaller depths and a greater hydrodynamic drag (induced by vegetation) (Wolanski et al., 1980; Furukawa, 1997). Hence, most water in the channel/flats system is transported via the channel. During overbank tides, velocities in the channel must increase in order to transport these larger volumes of water. These 'mass conservation' type effects are complicated by 'momentum conservation' effects. When the intertidal flats are inundated, the propagating tidal wave is also slowed and deformed (Aucan and Ridd, 2000; Fortunato and Oliveira, 2005). This can produce temporarily high water surface slopes (i.e. spatial differences in water levels), both along the channel and between the channel and the flats. These water surface slopes can induce strong accelerations in flow velocities. Figure 3 shows a water level and velocity time series from a site in Yalimbah Creek, collected in October 2008 (Figure 1b). Notice how the peak velocities are much higher during overbank tides than within bank tides. We will now develop a crude model of this data set, based only on mass conservation considerations. To do this, assume that: 1) the water surface elevation in the channel/flat system is constant in space; 2) that the flats receive all their water from nearby parts of the channel, and 3) that there is no inflowing fluvial discharge. Although these assumptions are a strong simplification of reality in many situations, they lead to simple calculations, and are accurate in some situations (see below). At any cross-section in the creek, the discharge in the channel Q_c must be equal to the rate of change in water volume upstream (dVol/dt). Thus, Q_c= dVol/dt = (dVol/dh)*(dh/dt) where the last step follows from the 'chain rule' for differentiation. Because the average velocity at this site in the creek is v_c = Q_c/A_c (where A_c is the channel cross-sectional area), it follows that: v_c = [ (dVol/dh) / A_c ]*(dh/dt) = F(h)*dh/dt where F(h) = [(dVol/dh) / A_c]. The assumptions mean that F(h) is purely a function of h (and the location of the cross-section). Qualitatively, this equation says that the velocity in the creek can be predicted purely from a water elevation time series, by estimating dh/dt (the rate of change of the water level), and F(h). Although the latter is unknown, it can potentially be estimated with morphological data, or statistically as a high order polynomial of h (using a time series of water levels, and velocity at the site). Does this work for Yalimbah Creek? Figure 4 shows the predicted and measured water velocities over a few tides at the 'velocity measurement' site in Figure 1b, using water level data from a site in Number One cove (Figure 1b). The model does a decent job of predicting the velocities during smaller, within channel tides. It also qualitatively predicts the velocity peaks during overbank tides. However, it incorrectly estimates the magnitude of the flood velocity peaks, and the final ebb velocity peak. It also poorly estimates the timing of the ebb velocity peaks. These results are consistent with the hydrodynamic theory reviewed above. During within channel tides, water slope effects are relatively slight, and so the 'flat water surface' model does a good job at predicting the within channel velocities. During overbank tides, the model is able to qualitatively fit the velocity peaks as the flow goes overbank. However, momentum effects make the simple 'flat water surface' approximation rather crude at this time, and the velocity is not simply a function of h and dh/dt at the mouth. Thus, the results are not as good. Another likely source of error is the assumption that the measured velocity time series reflects the mean within-channel velocity. In reality, variations in velocity over the cross-section mean that this will not always be a good approximation. However, continuity-based models have the advantage of simplicity. They can also be extended to two dimensional flows (Fagherazzi, 2002; Fagherazzi et al., 2003). Results from the latter studies also suggest that they perform well in some situations. However, it is important to realise that some basic features of tidal hydrodynamics cannot be explained while ignoring flow momentum conservation. This includes the asymmetry of tidal currents. While much is known about such processes, to understand them you will need to consider the principles of momentum conservation, as well as mass conservation.