IC1_I

Initial Research Questions and Objectives of the Project

Sediment transport on beaches is primarily driven by the action of waves and wave-induced currents. Nearshore circulation is therefore important in determining many shoreline and nearshore features over small- (e.g. beach cusps), medium- (e.g. nearshore sandbars) and large-scales (embayments and open coasts) (Short, 1996). Nearshore circulation patterns have been extensively studied on long, open coasts, with much attention paid to describing rip current circulation patterns within the surf zone (MacMahan et al., 2010) and reproducing nearshore flow pattern using numerical models (Castelle and Ruessink 2011). Much of the world’s coastline, however, consists of embayed beach environments (Inman and Nordstrom, 1971; Short and Masselink, 1999), whereby sediment is restricted from moving parallel to the shoreline by hard structures protruding from the land, such as naturally-occurring headlands or man-made breakwaters. Embayed beaches differ from open-coast beaches because of the manner in which flow and sediment transport processes are restricted by the underlying geometry of the embayment (Short, 2010). Circulation patterns within embayments are generally recognized to differ significantly from open coast circulation, with increased cellular circulation resulting from the presence of headland structures (Short, 1996; Loureiro et al., 2012).

Embayed beaches typically form a curved planform which has been characterized empirically by many researchers (Krumbein, 1944; Silvester, 1960; Yasso, 1965, Hsu and Evans, 1989; Silvester and Hsu, 1993; Moreno and Kraus, 1999). Despite their relatively stable long-term form, they are prone to problems arising from seasonal or short-term (storm duration) beach rotation events (Klein et al., 2003; Harley et al., 2011). Additionally, much of the current concepts related to beach evolution, bulk sediment transport (e.g. the CERC formula) and data reduction methods are geared towards open-coast beaches rather than embayed beaches (Bruun, 1962; USACE, 1984; de Vriend et al. 1993). Early research on embayed beaches focused on equilibrium planform concepts which relate the formation of the curved planform to a single (representative) wave direction and the effects of wave diffraction. More recently, numerical simulations of wave-driven circulation within embayments have reproduced the development of circulation cells around headland structures and within the embayment (Pattiaratchi et al., 2009; Silva et al., 2010). Additionally, sophisticated process-based morphodynamic models have been used to simulate the development of nearshore rhythmicity induced by rip currents (Reniers et al, 2004; Castelle and Coco, 2012). These numerical studies, however, are restricted to a relatively short time frame (timescales in the order of days to months) and feature embayments with limited curvature.

The objectives of the thesis are mainly two-fold. Firstly, the long-term stability (O ~2–50 years) of embayed beaches will be studied in order to determine what key physical processes are responsible for their formation (Daly et al., 2011). These studies will focus on beaches with high curvature and with a defined shadow zone in the lee of the main headland structures. As previously mentioned, diffraction has typically been assumed to be the dominant wave-driven process responsible for shaping embayed beaches (LeBlond, 1979, Silvester, 1985). This hypothesis will be tested, and additionally, the role of wave dissipation and directional spreading. As most embayed beaches already exist in a physically mature form, this topic cannot be studied using regular observational methods, which has therefore meant that it has never been fully studied before. The best approach to accomplish this goal is by using a process-based morphological model to simulate the natural evolution of an embayed beach over time until it forms a stable shape. From such a study, we can determine (1) the role of wave-driven processes in the formation of the typically curved embayed beach shoreline, and (2) the development of flow and transport patterns within the embayment and possible enhancement or restriction of the morphological evolution caused by changes in the geometry of the bay.

The second main objective of the thesis is to study the seasonal and short-term changes in the morphology of embayed beaches, which will be heavily influenced by the local wave climate. The wave climate in many parts of the world can be quite complex. Some locations may have more than one dominant wave direction (bi-modal), while others may be frequently affected by storm conditions from random directions (e.g. hurricanes). By using only the predominant wave direction for equilibrium studies, as is commonly practiced (Gonzalez and Medina, 2001; Jackson and Cooper, 2010; Oliveira and Barreiro, 2010; Schiaffino et al., 2011), the effect of other potentially morphologically significant wave events is ignored. This is usually countered by including a component of directional spreading which is generally centered around the predominant wave direction, however, this may not adequately reflect the actual true variability of the wave climate. Additionally, the wave climate may also have a variable distribution of wave energy classes. As such, the wave climate should be discretized into a finite number of representative wave conditions in order to account for its variability. Data reduction methods (e.g. de Vriend et al. 1993) can be applied to obtain these conditions; however, most have only been tested on open-coast beach systems and are not applicable to embayed beaches. A different method to determine the equilibrium bathymetry of an embayed beach will therefore be tested by taking into account the discretization of wave directions and wave energy, and finally, using a predetermined sediment transport capacity to weigh the influence of each representative wave condition.

After successfully completing the above step, further investigations will be done to determine (1) the association between pre-existing beach states and the changing wave climate, and (2) the effect of the sequence of wave events on the resulting morphological changes. To accomplish this, a nine-month field survey at the Tairua and Pauanui beaches in New Zealand was planned and executed, wherein beach profiles, sediment samples and wave data were measured at high temporal and spatial resolution. The collected field data is used together with, for case (1), an empirical shoreline model (Yates et al., 2009) for comparison of measured and predicted data. This highlights the potential reaction of the beach based on its pre-existing state and the immediate wave conditions. For case (2), a process-based morphological model will be used to simulate the changes occurring on the beach using the developed input reduction technique. The sequence of wave conditions will be changed to observe differences in the resulting morphology of the bay. These studies together will highlight the key factors controlling both long- and short-term morphological changes on embayed beaches.

Description of Achieved Results

The processed-based morphological model, Delft3D (Lesser et al., 2004), was used in all simulations. The model is capable of simulating wave-induced flows and the resulting morphological changes. The wave module, SWAN (Booij et al., 1999), includes a phase-decoupled approximation of diffraction (Holthuijsen et al., 2003). Sediment transport was computed according to van Rijn (1993) and the resulting morphological changes were accelerated using a morphological scaling technique (Roelvink, 2006).

With regard to the first objective of the thesis research, results obtained from the numerical simulations indicate that wave diffraction is a less important process when compared to directional spreading and changes in the peak wave direction. Increased turbulence in the wave breaking zone, simulated using a wave roller formulation, increases the morphological activity in the bay, primarily by transporting turbulence into the shadow zone. The variability of wave directions is, therefore, also a key factor in defining the shape of an embayed beach, rather than the dominance of a particular wave direction. Only by changing the peak direction will the energy distribution within the bay be affected. This is usually manifested in nature as storm events. It is therefore shown that these events are necessary in order to maintain the curved shape of the beach.

It has been shown that the morphological evolution of an embayment can be approximated to an exponential function. As such, area-doubling periods can be defined and used as averaging windows. These windows highlight equivalent morphological periods irrespective of the forcing conditions or geometry of the embayment. Therefore, the development of flow and transport patterns can be inter-compared between different simulations. What is clearly shown in all simulations is the transition from a rotating form of shoreline development to a translating form of shoreline development. This is mainly the result of reduced long-shore velocities (and transport) over time, together with an increase in the relative importance of cross-shore flow (and transport). The headlands play an important role in trapping the circulation cells within the embayment, thereby stabilizing further development of the bay. The transition from an export oriented to a self-sufficient system generally occurs once the surf zone width is equal to the up-coast headland length, which results in changes in the flow and transport patterns and ultimately causes a curved shoreline. The area-doubling period has also been shown to be a characteristic of both wave forcing and bay geometry. This allows parameterization of an expected bay shape in relation to a number of significant variables, particularly wave height, sediment size and bay width.

With regard to the second main objective of the thesis research, a method to determine the equilibrium bathymetry has been tested and presented. The method discretizes the wave climate (4 years duration) into a large number of individual wave conditions (IWC) (240 conditions), and the sediment transport capacity for each IWC is determined from numerical simulations over an arbitrary initial bathymetry. From this, the IWCs are grouped into uniform directional bins and subdivided into several representative wave conditions (RWCs). Morphological simulations of 8 or more RWCs and with 6 or more wave directional bins compare well to measured data. These simulations will be extended to look at changes over a longer period (40 years), noting the differences in both the medium-term wave climate and the resulting changes in the equilibrium morphology.