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Before investigating the hydrodynamic modelling of natural floodplains it is necessary to determine what constitutes the floodplain area. Natural floodplains are generally typified by areas of shallow water flows and they are generally governed by bed shear as well as resistance due to drag imposed by vegetation. As mentioned earlier, most of the vegetation has contributed a lot to alter the overall physical characteristics of the natural floodplains and consequently generated hydraulic obstructions to the floodwater flows. For example, floodplains in estuaries are basically populated by a diverse range of species, with reed phragmites being quite

typical for Britain (Purseglove 1989), cypress swamps in the United States, and mangrove swamps in subtropical and tropical climate countries.

Although the type of vegetation and the climate may vary, the basic hydrodynamics of floodplains are essentially similar, with shallow water flows and vegetation both providing drag, as well as blocking to the flow. The main differences are whether the vegetation penetrates the surface of the water and if it is subject to bending due to the force of the flow exerted upon it. There are of course other geometric differences, such as whether the vegetation is bushy or stem like, and the typical dimensions such as maximum diameter of the stem. Other considerations for modelling the hydrodynamic of natural floodplains include: whether the vegetation typically grows in dense well distributed populations, or whether the vegetation tends to be randomly distributed and mixed, or even if the vegetation stems are managed and therefore are of average geometrical properties and density.

Overall one of the key elements to be considered in hydraulic modelling of natural floodplain is the selection of hydraulic roughness involved. In the past, Chow (1959) adopted the empirical relationship between bed friction and depth of flow as in the Manning equation, and then simply adapted the friction coefficient to encompass an empirical value for the vegetative roughness, which may vary from 0.03 for short grass to 0.1 for dense trees. Eventually, this roughness can vary significantly in different parts of the system, even within the channel or floodplain (Robert et al., 1992). In fact, this method is having some limitations for the applications in shallow water flows for floodplains and apparently it is subjective to practical experience, and therefore less useful for inclusion in numerical models. However, this method may be appropriate for the general engineering stage of design and analysis.

In the present study, the topic of analysing and modelling the flow through vegetation has been the subject of much research, to varying degrees of details (such as investigations by Wolanski et al., 1980; Sengupta et al., 1986; Kadlec, 1990; Ridd et al., 1990; Nepf, 1999; Choi, 1999; Wu et al., 2001; Struve and Falconer, 2001;

Struve et al., 2003; Wilson, 2007; etc.). Most of the research undertaken to date for the finer analysis of vegetative effects has used the assumption that vegetation is well represented as a simple cylindrical obstruction (Li and Shen, 1973; Petryk et al., 1975;

Pasche and Rouve, 1985; and Kadlec, 1990).

Besides this assumption, in most types of this research study, the common theme has always been that the important term which required defining was the drag factor attributable to the presence of vegetation. The drag force caused by vegetation is considered as a key hydraulic parameter in determining flow resistance for natural floodplains. In numerical modelling, many researchers have utilised the mathematical equation, with an additional drag force term, so that the resistance due to emergent vegetation could be modelled and accordingly a drag coefficient is required hereafter.

This drag coefficient relates to the shape of the boundary layer around the vegetation elements, which are subject to changes in the diameter and geometry of the individual vegetation form.

Petryk et al. (1975) considered the influence of the drag force introduced by vegetation on the flow structure, with the drag force effect through the vegetation being incorporated into the Manning coefficient; and vegetation resistance being proportional to the projected surface of the vegetation in the flow direction. Some research studies have focused on modelling the effects of vegetation on flow mechanisms and resistance in more detail, for examples depth dependent vegetation

effects (Fathi-Mahagdahan et al., 1997; Kutija et al., 1996); and the spatial distribution and hydraulic interactions between the vegetation elements (Naot et al.,

1997). On the other hand, Furukawa et al. (1997) addressed that vegetation was responsible for enhancing friction, with much of this enhancement being due to the vegetation presenting obstacles to the flows. These obstacles generated complex two- dimensional currents, with jets, eddies and stagnation regions, as well as vegetation scale turbulence.

In modelling vegetation as a cylinder, with the consideration of a drag force, Nepf (1999) introduced a dimensionless population density (AD = D2IS1), where A is the projected area per unit volume; D is the cylinder diameter; and S is the mean spacing between cylinders. The study suggested that the drag coefficient for a single cylinder in a two-dimensional flow is about 1.0 at the Reynolds number of 1000. For a group of cylinders, the drag coefficient for different cylinders could be different due to the wake characteristics, and probably decreases as the vegetation population density increases. For cylinder Reynolds numbers between of 4000 to 10000, Nepf (1999) showed that the drag coefficient decreased roughly from 1.2 to 0.6 as the population density increased from 0.008 to 0.07 respectively. Based on this study, the drag force was mainly found to be dependent upon the cylinder geometry, cylinder displacement, cylinder density and flow conditions. The turbulence intensities increased as the population density decreased, but decreased as the population density increased (Nepf, 1999).

As previously mentioned the majority of subsequent research undertaken has used the assumption that vegetation is well represented by a cylinder. Accordingly, most of the research has been in the development of algorithms for analysis of the

finite effects of single and multi wakes of cylinders for simplification. Figure 3.3 shows the pattern of flow around a bluff shape (i.e. a cylinder) and presenting the low pressure zone at the rear body draws in fluid from further out in the boundary layer, where the pressure is higher, consequently forming the wake zone, as well as powerful eddies which are generated and carried downstream. However, it should be noted that in making this cylindrical assumption for ideal vegetation, certain governing factors of the hydrodynamics of the real environment have been neglected.

Y

!

‘negative' velocities (separated flow)

___ _

w ake

low pressure

Figure 3.3 Flow around a bluff shape (Chadwick et al., 2004)

In taking account of all the assumptions and considerations herein, and in extending the previous research work undertaken by Struve (2000), Westwater (2001), and Wu et al. (2001), for the purpose of this study, an existing two-dimensional numerical model has been refined to investigate further the hydrodynamic processes of natural floodplains, with the focus on mangroves as the main hydraulic

obstructions to floodwater flows. It was the refinement of an existing hydrodynamic model, with which this research study was primarily concerned, and this model has been calibrated and validated with the data from the laboratory experimental work, previously carried out by Westwater (2001) on a model floodplain with the main channel running through the centre. Detailed investigations into modelling the hydrodynamics of natural floodplains with mangroves will be carried out in the next chapter. The study will also focus on investigating the consequential impact of mangroves on the dissipation of extreme flood events, and in particular on tsunamis.