The chlorophyll fluctuation spectrum in the sea1,2

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Abstract
The spatial heterogeneity of phytoplankton abundance in the sea is controlled both by the turbulent motions of the water and by the rate of reproduction of the organisms themselves. An expression is derived for the shape of the chlorophyll fluctuation spectrum as a function of wavenumber based on an approach first used in the study of reacting mixtures in a turbulent fluid. Unlike an earlier version, this spectrum has a maximum value at a wavenumber km = (6rε−1/3/5)3/2, where r is the rate of growth of the phytoplankton and ε is the rate of dissipation of turbulent kinetic energy. For wavenumbers k ≫ km the spectrum is proportional to k−5/3, not unlike that for a passive scalar such as temperature. The significance of the existence of the spectral peak is that it implies a preferred size for phytoplankton patches in the sea. For typical oceanic conditions, km−1 ≈ 5–10 km.

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