**4.3 Gyre analysis**

The horizontal expansion and contraction of gyres were measured to quantify the extent of bay fluctuation. Tracks produced by the RMATRK model were of three categories:


The Hydrodynamic Modelling of Reefal Bays –

model results.

the overall variability.

**5.2.1 Current flow** 

**5.2 RMA model simulations** 

Placing Coral Reefs at the Center of Bay Circulation 163

0.62) than the eastern arm currents (cross correlation r = 0.18) with channel currents. The west reef feeder currents therefore contributed much more to channel flow than the east reef. Multiple regression values showed that the back-reef currents combined accounted for 47% of the variability in the channel currents, compared to wind and tides accounting for 29%.

Fig. 4. Current component plots are shown for the east back-reef (a), the west back-reef (b) and channel (c) of Wreck Bay, collected from long-term deployment of S4 current meters moored at all three sites at the same time. This field data compared favorably with RMA

Accountability by winds and tides of the overall variability in the current magnitude decreased from highs of 55-56% for the spring and winter data to 29% for the summer currents. During this summer period the lowest recorded mean channel current speed (7.7 cm s-1) was observed as well as an equality of the relative contributions of tides and winds to

Velocity results from S4 current meters compared well with RMA model results (depth averaged) for the dominant north (Y) component of the channel site at Wreck Bay (Figure 5), giving no significance for difference by t-test. For the month of August (2000) , S4 north component readings averaged -7.8 cm s-1 while the RMA model averaged slightly lower at - 8.2 cm s-1 (Table 2). The north component was used to represent the channel flow given its

high cross-correlation value of -0.99 with the channel flow magnitude.

 Indefinite tracks: where one set of particles was tracked for as long as they remained in the reefal bay system - their paths plotted for every three hours they remained.

Hourly plotted tracks were used to predict the duration of a reef gyre. Three-hourly tracks were plotted to capture the full horizontal extent of the circulation.

Fig. 3. Diagram of the reefal bay dimensions used in calculating the circulatory extent of the bay. The extent (BC) is calculated as a fraction of the AC distance normal to a line (DE) joining the land projections. AC is derived from an elliptical approximation of the outer, seaward curve of the looping currents.

Extents were measured from these plots as a proportion of the linear distance, from the shore to the elliptical arc, normal to a straight line joining the land projections at the ends of the bay indentation (Figure 3). The ellipse best approximates the seaward edge of the gyre. The elliptical major axis is always equal to or greater than the length of the straight line joining the land projections. Therefore, the reef circulation lateral extension, *Lc*, is given as the percentage:

$$L\_c = \frac{BC}{AB} \times 100\tag{3}$$

Indefinite tracks allowed predictions of the retention ability of gyres. The number of particles remaining around the reef was counted after each 3-hr track run.
