A physical derivation of nutrient-uptake rates in coral reefs: effects of roughness and waves

Mass-transfer rates between water and benthos are derived based on the dissipation of energy by the benthic communities of coral reefs. Roughness of the benthic communities causes currents and waves to dissipate energy on reef flats at rates which far exceed ocean values of energy dissipation. The derivation here shows that first-order rate constants for nutrient uptake are (1) proportional to energy dissipation to the 0.25 root, (2) proportional to the bottom shear stress to the 0.4 root, and (3) proportional to current speed to the 0.75 root (decreasing to the 0.4 root under extreme wave activity). The shear stress, thus nutrient uptake, is positively correlated to the large-scale roughness, and to excess wave height (above the breaking height) of incoming waves. These causal relationships between nutrient-uptake rates and dissipation of energy support the general observations of reef zonation and reef metabolic rates, and are the paramount reason that coral reefs can maintain high productivity in low-nutrient tropical waters.