Minimum length scale for growth-limited oceanic plankton distributions

A patch of phytoplankton in a shear environment will be drawn out into a long ribbon-like structure or filament. Phytoplankton are typically growth-limited due to nutrient limitation or grazing pressure. For such a reactive tracer it is demonstrated that there is a minimum filament width representing a balance between a diffusion and growth fuelled outward-propagating wave and the opposing shear flow. The minimum width is given byW=8.6κλ max1, 0.4μλ−1.6+1where κ is the effective diffusivity for scales small compared to the filament width, λ the straining rate of the flow, and μ the net tracer growth rate. Two regimes are apparent with behaviour governed by the ratio of biological growth rate to the strain rate. Counter-intuitively, for μ/λ>2.5, the minimum width exceeds that for an unlimited exponentially-growing tracer by a factor of 0.4√(μ/λ)+0.36. For μ/λ<2.5 the behaviour mimics that of an exponentially-growing or inert tracer with filament width independent of growth rate. The results demonstrate that predictions of the finest scale of structure seen in patchy phytoplankton distribution are very sensitive to the biological processes active and their representation.