The minimum length-scale of oceanic phytoplankton distributions

Abstract

Starting from the simplest approximations a hierarchy of numerical models is developed with the intention of improving understanding of how biological and physical mechanisms interact in producing observed structure in plankton patches. Specifically how small scale mixing, strain and growth combine in determining the minimum equilibrium length-scale of phytoplankton filaments. We expand upon a previous study of an exponentially growing tracer in a uniform strain flow to investigate the behaviour of a logistic tracer, a more appropriate approximation of bulk phytoplankton population dynamics. A new equation to describe the minimum expected length-scale is derived. The effect of explicit nutrient representation is also considered. This is not found to affect patch size, although a striking effect on crosssectional profile is observed under certain conditions. We test the derived formula in a more realistic and hence more complex physical environment (a two-dimensional turbulent flow). We investigate inert and logistic growth tracer dispersal and consider the effectiveness of the previously derived formula for predicting minimum length-scales. In addition to inert and logistic growth tracer models we also consider a more sophisticated ecosystem model and assess the propriety of using a logistic tracer for investigations of mesoscale phytoplankton patchiness. An aside is taken to determine the best measure of strain when investigating plankton patch dynamics. A comparison is made of techniques used in comparable previous studies of tracer dynamics and recommendations made for future investigations. Errors resulting from mis-sampling of the tracer field are also considered. These results are intended to provide recommendations when considering oceanic tracer dispersal and calculation of mixing parameterisations. The 'best case' scenario is investigated throughout hence all results provide a robust upper limit of what is possible observationally.

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