Mass-transfer-limited nitrate uptake on a coral reef flat, Warraber Island, Torres Strait, Australia

Abstract

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.

Appendix A

The one-dimensional equation for depth-averaged flow across the reef flat may be written as:

$$ \frac{{\partial U}} {{\partial t}} + U\frac{{\partial U}} {{\partial x}} = g\frac{{\partial \eta }} {{\partial x}} + \frac{{\tau _{w} }} {{\rho d}} - \frac{{\tau _{b} }} {{\rho d}} $$

(A1)

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:

$$\tau _{{\text{b}}} = \rho C_{{\text{D}}} U^{2} $$

(A2)

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:

$$\tau _{{\text{w}}} = \rho _{{\text{a}}} C_{{\text{a}}} w^{2} $$

(A3)

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:

$$gU\frac{{\partial \eta }} {{\partial x}} = \frac{{C_{{\text{D}}} U^{3} }} {d} = \varepsilon $$

(A4)

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.