A detailed description of the model along with the validation tests that were performed can be found in Richardson (1995b,c). The required vertical and horizontal resolutions were discussed there in the context of boundary layer theory to ensure that the shearing stresses were adequately resolved. To summarize, minimum horizontal and vertical resolution were determined by simulating a Blasius boundary layer (Schlichting 1979) and by examining the friction coefficient (or local drag) along a flat plate (Kreith and Bohn 1993). It was found that the boundary layer velocity profile was adequately resolved when the first grid point was 1 mm from shield surfaces and when 1-mm gridpoint spacing was used on the shield. Simulations using a finer grid resulted in the same solution, demonstrating that a grid-independent solution had been obtained.
An example of a 2D unstructured grid used for simulating flow through a Gill shield is shown in Fig. 6a. Shield dimensions are the same as a standard Gill shield:0.12-m diameter, with 0.16-m-high and 0.002-m-thick plates. Each triangle represents a computational cell with the most cells concentrated near the shield plates in order to represent the boundary layer shearing stresses. The entire computational domain was approximately 2.5 m long and 2.25 m high, which provided many shield diameters between the shield and boundaries to reduce their effect on the flow. Air enters the domain from the left at a specified velocity and exits the domain on the right. The top and bottom boundaries are free slip and rigid.
Commonly, the upper boundary of the DBL is determined by the intercept between the linear concentration gradient and the constant part of the O2 profile, representing the bulk concentration in the free-stream water aloft5. The lower boundary in this study was the coral surface, but only for the case of no cilia activity. Shapiro et al.4 showed that ciliary vortices modified the oxygen transport in the lower boundary layer, creating curved or S-shaped profiles that indicate an effective mass transport coefficient significantly larger than the molecular diffusion coefficient. For flux calculations we therefore used the linear part of the profiles above the vortices, a layer we refer to as upper DBL, where particle tracks indicate a laminar, plane parallel flow (see results below) and in which a predominantly diffusive transport can be assumed. We further assume that oxygen is neither produced/consumed in the vortex layer nor in the upper DBL so that the oxygen flux across the two adjacent layers is equal and ultimately represents the flux between coral and ambient water. 2b1af7f3a8