**1. Introduction**

Reefal bays are a common type of bay system found along most Caribbean coasts including the Jamaican coastline. These bay systems are associated with and delimited by arching headland with sub-tending reef arms broken by a prominent channel. Traditionally, these bays are termed "semi-enclosed" as their limits are defined by the sand bar or reef partially cutting off waters behind them from open sea (Nybakken, 1997). Yet, it has been shown that circulatory patterns emanating from the lee of reef structures can persist beyond the forereef (Prager, 1991; Gunaratna et al., 1997). This raises the possibility of re-characterizing these systems where the reef is defined as the centre of a dynamic bay, inducing a continuous re-circulation of the inside waters beyond the traditional limit (Figure 1). In this study, hydrodynamic modelling, particle tracking and a novel gyre analysis method were used to assess the reefal bay's signature spatial and temporal patterns in circulation, with the goal of characterizing the reefal bay as unique in its function. This was carried out on the Hellshire southeast coast of Jamaica where four of seven bays are typical reefal bays.

Fig. 1. A number of hypothetical bays are presented where A represents the open bay, B the traditional definition of the reefal bay, and C the reef proposed as circulatory centre of the reefal bay system.

Reef systems often function to reduce the shoreline wave action and influence sediment dynamics. They therefore provide the ecological link between land and sea, as nurseries offering protection for marine life, as recreational sites, and as receiving sites for industrial

The Hydrodynamic Modelling of Reefal Bays –

conditions where waves no longer break over the reef.

finite element-based model for stratified flow.

seeps into the bays (Goodbody et al., 1989).

**3. Reefal bay sites** 

two reefal bays.

Placing Coral Reefs at the Center of Bay Circulation 157

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

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

Southeast of Jamaica, a 15 km stretch of coastline, the Hellshire east sector (Figure 2), consists of seven bays - four of which are reefal. Three bays were compared for their circulatory signatures – Wreck Bay, Engine Head Bay and Sand Hills Bay. Two of the three, Wreck Bay and Sand Hills Bay, have prominent reef parabola stretching between headlands with a central, narrow channel breaking the reef continuum. Wreck Bay, with its narrower channel, is more enclosed than Sand Hills Bay. Associated reefs are emergent and exposed, more so at low tide. Both reefal bays are separated along the coastline by Engine Head Bay, an open bay with no development of reef arms. Engine Head Bay was therefore considered as a control given it is non-reefal and its position exposes it to the same conditions as the

A diurnal variation in the wind records is typical of the southeast coast of Jamaica (Hendry, 1983) due to the influence of the sea-land regime. The tidal range is microtidal ranging from 0.3 - 0.5 m with an annual mean of 0.23 m (Hendry, 1983) and demonstrating a mixed tidal regime. Tidally generated currents are therefore small in amplitude compared to winddriven currents. The wave climate of the southeast coast is influenced mainly by trade wind-generated waves that approach Jamaica from the northeast. Offshore waves impact the shelf edge off Hellshire from a predominantly east-south-easterly direction after undergoing southeast coast refraction. Swell waves approach the coast at a typical period range of 6-9 seconds, but these are soon affected by complex bathymetry. Wave decay occurs when the land-breeze emanates along the coast. The shelf along which these bays fringe are made up of basement rock composed of Pliestocene limestone eroded during low sea levels in the Pliestocene epoch. As a result, bathymetric highs are now shoals, banks, reefs and cays, and on the inshore, karst limestone relief facilitates freshwater sub-marine

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 unique.

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 dynamics and responsible forcing functions.
