On the theory of advective effects on biological dynamics in the sea. III. The role of turbulence in biological-physical interactions

Abstract

A nonlinear model for biological and physical dynamical interactions in a laminar upwelling flow field in parts I and II of this study is extended to turbulent flow. In the previous studies, a prescription for obtaining quadrature solutions to the fundamental biodynamical equations was developed. In this study, we use a probability density function approach on these solutions to obtain statistics of the biodynamical state variables and their self-interaction for the case of turbulent advection. To illustrate the theory, a simple nutrient (N), phytoplankton (P) problem is considered, that of upwelling into a surface turbulent layer. Biological interaction is modelled as bilinear, representing the uptake of N by P in a uniform light euphotic zone. A random walk model is used to obtain the appropriate probability density function for the advective turbulent field. The mean quantities, N̄,P̄, as well as the biological interaction term F̄ = 〈NP〉 are calculated. The term F̄ has two contributions, (N̄P̄), and the turbulence-induced interaction term 〈N′ P′〉. It is shown that the often neglected turbulence-induced coupling term 〈N′ P′〉 is of the order (N̄P̄) and opposite in sign. This results in, over a wide range of Peclet numbers, the mean interaction term 〈NP〉 being significantly smaller than either of its constituent terms, (N̄P̄) and 〈N′ P′〉. © 2007 The Royal Society.