**2. Numerical modelling development and challenges for reef systems**

The lagoons formed by coral reefs exhibit some of the most variable bathymetry of coastal oceanography and present a challenge to understanding their dynamics (Hearn, 2001). The ideal model must be able to account for all the forcing factors and conditions typical of the coral reef environment including wave and current propagation and interaction, density flows, channel exchange, reef topology and reef morphology. The modelling becomes even more complex when attempts are made to process spatial scales ranging from tens of kilometers down to sub-meter at the same time. These difficulties continue to confound localized studies of reef phenomena.

Several numerical models have been applied to lagoon hydrodynamics using onedimensional (Smith, 1985), two-dimensional (Prager, 1991; Kraines et al., 1998) and threedimensional models (Tartinville et al., 1997; Douillet et al., 2001). Wave breaking and overtopping remain phenomena that are difficult to describe mathematically because the physics is not completely understood (Feddersen & Trowbridge, 2005; Pequignet, 2008). The

and biological effluent. Their distinctive circulatory patterns have, however, been understudied and not fully characterized. This research aims to describe the signature circulatory patterns of the subtending reef bay system, including the effects of bathymetry, wind, tides and over-the-reef flow on this circulatory emanation. Hydrodynamic modelling, particle tracking and a novel gyre analysis method were utilized to characterize the reefal bay circulation and determine those features that make this reef-centered bay system

Reefal bays carry unique patterns of circulation, however, very few reef hydrodynamic studies have focused on the particular circulation associated with fringing Caribbean reef systems. One study on a shallow, well-mixed Caribbean type back-reef lagoon in St. Croix documents that circulation was dominated by wind and over-the-reef flow (Prager, 1991). Another study on the Grand Cayman Island reefs documented that the outer reef tended to be dominated by wind-driven currents and the inner by high frequency waves. Deep water waves and tides, winds and over-the-reef flow controlled the hydrodynamic sub-system found in the lagoon (Roberts et al., 1988). At the reef crest, wave breaking and rapid energy transfers resulted in a sea level set-up which drove strong reef-normal surge currents (Roberts et al., 1992). In both the Grand Cayman and St. Croix reef systems, flow over the reef was often the dominant forcing mechanism driving lagoon circulation (Roberts, 1980; Roberts & Suhayda, 1983; Roberts et al., 1988). Whereas previous studies have contributed to Caribbean reefal hydrodynamics, their application to the reefal bay systems in particular falls short in a number of ways. The reefal bay dynamics has never been distinguished from other reef systems as a unique coastal system. It is instead often broadly categorized under the larger fringing reef system or as a fully enclosed lagoon system. Also, the contribution of reef-induced eddies to the hydrodynamic make-up is understated. Smaller-scale eddy features were not examined in these Caribbean studies. These are important features to note, whether transient or permanent in nature (Sammarco & Andrews, 1989) because of their ability to trap water, sediments, larvae and plankton around reefs. Sammarco & Andrews (1989) showed that attenuation of tidal effects within lagoons and tidal anomalies generated by the reef were responsible for creating or maintaining eddies on isolated systems. More comprehensive research is now necessary to determine the characteristic circulatory

**2. Numerical modelling development and challenges for reef systems** 

The lagoons formed by coral reefs exhibit some of the most variable bathymetry of coastal oceanography and present a challenge to understanding their dynamics (Hearn, 2001). The ideal model must be able to account for all the forcing factors and conditions typical of the coral reef environment including wave and current propagation and interaction, density flows, channel exchange, reef topology and reef morphology. The modelling becomes even more complex when attempts are made to process spatial scales ranging from tens of kilometers down to sub-meter at the same time. These difficulties continue to confound

Several numerical models have been applied to lagoon hydrodynamics using onedimensional (Smith, 1985), two-dimensional (Prager, 1991; Kraines et al., 1998) and threedimensional models (Tartinville et al., 1997; Douillet et al., 2001). Wave breaking and overtopping remain phenomena that are difficult to describe mathematically because the physics is not completely understood (Feddersen & Trowbridge, 2005; Pequignet, 2008). The

unique.

dynamics and responsible forcing functions.

localized studies of reef phenomena.

large range of combinations of reef types, shapes, tidal environments and wave climates makes all existing analyses of wave-generated flow on coral reefs limited in their applications (Gourlay & Colleter, 2005). Instrument-measured field data, however, confirm that the wave dynamics is responsible for a significant proportion of the reefal lagoon/bay hydrodynamics (Symonds et al., 1995; Hearn, 1999, 2001). As the waves break, a maximum set-up occurs near the reef edge. The maximum set-up on the reef top is proportional to the excess wave height (Hearn, 2001). The set-up creates the pressure gradient required to drive the wave-generated flow across the reef (Gourlay & Colleter, 2005). Friction coefficients are also important to consider and so these are presented as large values in recognition of the great roughness of reefs (Symonds et al., 1995). In consideration, however, of reefs with steep faces where waves break to the reef edge, wave set-up is reduced by the velocity head of the wave generated current. In this case, influence of bottom friction in the surf zone is ignored. Wave overtopping has been developed and described as two linked functions by Van der Meer (2002):- one for breaking waves applicable to more intense wave conditions (here, wave overtopping increases for an increasing breaker parameter), and the other for the maximum achieved for non-breaking waves applicable to significantly reduced wave conditions where waves no longer break over the reef.

Three-dimensional models continue to evolve in simulating wave-driven flow across a reef. An attempt is made in this chapter to simulate the three-dimensional flow associated with reefal bays by incorporating equations for wave breaking and overtopping at the reef into a finite element-based model for stratified flow.
