Previous research has identified a relationship between the rate of dissipation of turbulent kinetic energy, ε , and the mass-transfer-limited rate of uptake by a surface, herein called the ε 1/4 law, and suggests this law may be applicable to nutrient uptake on coral reefs. To test this suggestion, nitrate uptake rate and gravitational potential energy loss have been measured for a section of Warraber Island reef flat, Torres Strait, northern Australia. The reef flat section is 3 km long, with a 3 m tidal range, and on the days measured, subject to 6 m s−1 tradewinds. The measured nitrate uptake coefficient, S , on two consecutive days during the rising tide was 1.23±0.28 and 1.42±0.52×10−4 m s−1. The measured loss of gravitational potential energy across the reef flat, ΔGPE , on the same rising tides over a 178 m section was 208±24 and 161±20 kg m−1 s−2. Assuming the ΔGPE is dissipated as turbulent kinetic energy in the water column, and using the ε 1/4 law, the mass-transfer-limited nitrate uptake coefficient, S MTL , on the two days was 1.57±0.03 and 1.45±0.04×10−4 m s−1. Nitrate uptake on Warraber Island reef flat is close to the mass-transfer limit, and is determined by oceanographic nitrate concentrations and energy climate.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Atkinson MJ (1987) Rates of phosphate uptake by coral flat communities. Limnol Oceanogr 32:426–435
Atkinson MJ (1992) Productivity of Enewetak Atoll reef flats predicted from mass-transfer relationships. Cont Shelf Res 12:799–807
Atkinson MJ, Bilger RW (1992) Effects of water velocity on phosphate uptake in coral reef-flat communities. Limnol Oceanogr 37:273–279
Atkinson MJ, Falter JL, Hearn CJ (2001) Nutrient dynamics in the Biosphere2 coral reef mesocosm: water velocity control NH4 and PO4 uptake. Coral Reefs 20:341–346
Atkinson MJ, Smith DF (1987) Slow uptake of 32P over a barrier reef flat. Limnol Oceanogr 32:436–441
Baird ME, Atkinson MJ (1997) Measurement and prediction of mass transfer to experimental coral reef communities. Limnol Oceanogr 42:1685–1693
Batchelor GK (1959) Small-scale variations of convected quantities like temperature in turbulent fluid. J Fluid Mech 5:113–133
Bilger RW, Atkinson MJ (1992) Anomalous mass transfer of phosphate on coral reef flats. Limnol Oceanogr 37:261–272
Bode L, Mason LB, Middleton JH (1997) Reef parameterisation schemes with applications to tidal modelling. Prog Oceanogr 40:285–324
Cowley R, Critchley G, Eriksen R, Latham V, Plaschke R, Rayner M, Terhell D—CSIRO Marine Laboratories Report 236 – Hydrochemistry Operations Manual. CSIRO Marine Laboratories Hobart
Dipprey DF, Sabersky DH (1963) Heat and momentum transfer in smooth and rough tubes at various Prandtl numbers. Int J Heat Mass Transfer 6:329:353
Hatcher BG (1988) Coral reef primary productivity: a beggar’s banquet. Trends Ecol Evol 3:106–111
Hatcher BG (1990) Coral reef primary productivity: a hierarchy of pattern and process. Trends Ecol Evol 5:149–155
Hearn CJ (1999) Wave-breaking hydrodynamics within coral reef systems and the effects of changing relative sea level. J Geophys Res 104:30007–30019
Hearn CJ, Atkinson MJ, Falter JL (2001) A physical derivation of nutrient-uptake rates in coral reefs: effects of roughness and waves. Coral Reefs 20:347–356
Li YH, Gregory S (1974) Diffusion of ions in seawater and deep-sea sediments. Geochim Cosmochim Acta 38:703–714
Nikuradse J (1933) Laws for flow in rough pipes. Forsch Arb Ing-Wes, Nr. 361
Odum HT, Odum EP (1955) Trophic structure and productivity of a windward coral reef community of Eniwetok Atoll Ecol Monogr 25:291–320
Richardson LF (1922) Weather prediction by numerical processes. Cambridge University Press, Cambridge
Sargent MC, Austin TS (1949) Organic productivity of an atoll. Trans Am Geophys Union 30:245–249
Smith SD, Anderson RJ, Oost WA, Kraan C, Maat N, DeCosmo J, Katsaros KB, Davidson KL, Bumke K, Hasse L, Chadwick HM (1992) Sea surface wind stress and drag coefficients: the HEXOS results. J Boundary-Layer Meteorol 60:109–142
Smith SV (1973) Carbon dioxide dynamics: a record of organic carbon production, respiration, and calcification in the Eniwetok reef flat community. Limnol Oceanogr 18:106–120
Tennekes H, Lumley JL (1972) A first course in turbulence. The Massachusetts Institute of Technology
Thomas FIM, Atkinson MJ (1997) Ammonia uptake by coral reefs: effects of water velocity and surface roughness on mass transfer. Limnol Oceanogr 42:81–88
Woodroffe CD, Kennedy DM, Hopley D, Rasmussen CE, Smithers SG (2000) Holocene reef growth in Torres Strait. Mar Geol 170:331–346
The generous support of the School of Mathematics, UNSW through the University Research Support Program and School travel funds is gratefully acknowledged. The authors greatly appreciated the hospitality of the Warraber people, in particular Clara Tamu and Bogo Billy, and Bill and Bev Stephens. We would like to thank Douglas Jacobs of the Torres Strait Regional Council for coordinating the project with the Warraber Council, David Terhill at CSIRO Marine Research who generously undertook the nutrient analysis, and Jean Rueger, UNSW, for the loan of surveying equipment. We would also like to acknowledge the generous help with theoretical aspects provide by Cliff Hearn and Eric Schulz, and Marlin Atkinson for inspiring this work. MB was funded by an Australian Research Council Postdoctoral Fellowship, and RB by a UNSW Goldstar grant.
Communicated by B.C. Hatcher
The one-dimensional equation for depth-averaged flow across the reef flat may be written as:
where U is the velocity across the reef flat, g is the gravitational acceleration, η is the sea level elevation, d is the depth, ρ is the density of water, τ w is the wind stress in the x-direction, and τ b is the bottom stress as a result of friction. A common relationship for the bottom stress is:
where the coefficient of drag, C D, depends on the roughness of the reef flat. The wind stress may be written in the same form:
where ρ a is the air density (~1.2 kg m-3), C a is the drag coefficient of airflow over the ocean surface, and w is the wind speed. C a depends on the roughness of the sea surface. A value of C a=1.0×10−3 from offshore measurements in small seas (Smith et al. 1992) has been used.
With values typical of Warraber Island reef flat of U ~0.2 m s−1, d ~ 0.8 m, ∂η/∂x~10−4 and w ~5 m s−1, a scaling analysis of Eq. (A1) shows that the two acceleration terms are of order 10−5, the wind stress terms is of order 5×10−5, and the pressure gradient term is of order 10−3. Thus to within 5%, the balance between pressure gradient and bottom friction terms reflects a steady-state flow in which acceleration and wind stress terms play no significant role.
The balance can be written in the form:
in which the left term represents the loss of gravitational potential energy and the right term the energy dissipation rate, where ε is the dissipation rate of TKE. Equation A4 can be used to obtain a value for C D.
About this article
Cite this article
Baird, M.E., Roughan, M., Brander, R.W. et al. Mass-transfer-limited nitrate uptake on a coral reef flat, Warraber Island, Torres Strait, Australia. Coral Reefs 23, 386–396 (2004). https://doi.org/10.1007/s00338-004-0404-z
- Coral reefs
- Nutrient uptake
- Torres Strait
- Great Barrier Reef