Application of the Robinson biodynamical theory to turbulence

Abstract

In the late 1990s Allan Robinson developed a theory of NPZ interactions in a laminar upwelling flow field. His approach was to use the advection reaction (AR) equation in a Lagrangian coordinate system. Recently, his theory was extended to turbulent flow by applying a probability density function to the solution of the AR equation. A review of this work is presented as well as new work examining the role of the turbulent induced biodynamical interaction (TIBI) effect, which is typically neglected in advection diffusion reaction (ADR) formulations for NPZ problems. The TIBI effect is associated with turbulence inducing fluctuations in nonlinear biological constituent interactions and is separate from the effect of turbulent mixing in dispersing the constituents. A simple example of the application of the theory – that of nutrient and phytoplankton fields being upwelled into a uniform optically active turbulent mixed layer – is presented. For this example, not including the TIBI term in an ADR formulation results in an overestimate of the primary production, increasing with decreasing turbulent Peclet number.