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Equations governing the variation through the flow field of averages of quantities such as species mass fractions, conditional on mixture fraction, are derived and modeled. The conditioning variable adds to the independent dimensions of the problem, but it is found that this is offset in some cases by reduction in the spatial dimensionality needed. Predictions are made for the reacting scalar mixing layer, and these show good agreement with experiment. The methodology effectively decouples the kinetics from the large inhomogeneity or macromixing aspects of the flow while preserving the input from the scalar dissipation or micromixing. Arbitrarily complex kinetics may be used within reasonable computational cost.

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To determine a Stanton number (St,, a dimensionless number giving the ratio of uptake rate to the rate of advection of the substance past the uptake surface) for a reef-flat community without the effects of wave surge, we placed communities of reef organisms in the bottom of a flume, 9.3 m long and 0.35 m wide. Water was pumped over the experimental communities at 13 different surface flow velocities, ranging between 2.3 and 58 cm s-l. Rate of phosphate (P) uptake at each velocity was measured by raising the ambient P concentration to -2 PM and measuring the rate of decrease in P concentration. St, for P uptake in the flume was significantly greater than estimates of St, derived from engineering studies of mass and heat transfer. This result confirms the finding of anomalously high mass transfer based on field data. Rates of P uptake increased as water velocity increased. The log of the first-order rate coefficient for P uptake was directly proportional to the log of velocity with a slope of -0.76. These results indicate that the rate of P uptake into reef benthos is controlled by diffusive boundary layers near the surfaces of organisms and that the surface geometry is such that improved transfer in comparison with engineering surfaces is obtained.We have shown elsewhere (Bilger and Atkinson 1992) that the rate of P uptake over a barrier reef flat was anomalously high compared to estimates based on engineering correlations for mass transfer. Part of the enhancement was attributed to the effects of wave surge currents; the remaining enhancement (a factor of -10) was attributed to the effects of high surface-area ratio (wetted area/projected area), the fractal nature of the surface, and roughness Reynolds number Rek and Schmidt number SC being higher than for the data range of the engineering studies. This large discrepancy was surprising. Hence it became important to verify high St, in a more controlled flow, without the effects of surge or reversing currents of the reef flat. Further if P uptake is mass transfer limited then P uptake into coral reef benthos should be positively correlated with water velocity. Here we report on flume experiments in which the velocity of water flowing over an experimental reef Acknowledgments

Reaction in a scalar mixing layer in grid-generated turbulence is studied experimentally by doping half of the flow with nitric oxide and the other half with ozone. The flow conditions and concentrations are such that the chemical reaction is passive and the flow and chemical timescales are of the same order. Conserved scalar theory for such flows is outlined and further developed; it is used as a basis for presentation of the experimental results. Continuous measurements of concentration are limited in their spatial and temporal resolution but capture sufficient of their spectra for adequate second-order correlations to be made. Two components of velocity have been measured simultaneously with hot-wire anemometry. Conserved scalar mixing results, deduced from reacting and non-reacting measurements of concentration, show the independence of concentration level and concentration ratio expected for passive reacting flow. The results are subject to several limitations due to the necessary experimental compromises, but they agree generally with measurements made in thermal mixing layers. Reactive scalar statistics are consistent with the realizability constraints obtainable from conserved scalar theory where such constraints apply, and otherwise are generally found to lie between the conserved scalar theory limits for frozen and very fast chemistry. It is suggested that Toor's (1969) closure for the mean chemical reaction rate could be improved by interpolating between the frozen and equilibrium values for the covariance. The turbulent fluxes of the reactive scalars are found to approximately obey the gradient model but the value of the diffusivity is found to depend on the Damköhler number.

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