Phytoplankton growth in oligotrophic oceans: Linear theory

Antonios Zagaris (June 28, 2011)

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In this talk, we will present analytic results concerning phytoplankton growth under nutrient-light co-limitation. The model we employ consists of two reaction-advection-diffusion PDEs for the plankton and nutrient concentrations and incorporates self-shading effects.

In the first part of this talk, we will work with a single spatial dimension (depth) and look closely into the linear stability problem for the trivial steady state (no phytoplankton). Using our results, we will identify the emergence of two distinct localized patterns: benthic layers (BLs), corresponding to the localization of plankton close to the bottom of the water column, and deep-chlorophyll maxima (DCMs), corresponding to localization in a thin region interior to the water column. This first part will close with an ecological interpretation of our findings.

In the second half, we will extend our model to account for an extra, horizontal dimension and include diffusion and (depth-dependent) advection along this new dimension. We will then investigate the corresponding linear stability problem and derive a condition for the relative sizes of horizontal diffusivity and advection, under which horizontally modulated DCMs may be expected to appear.