Simple mixing criteria for the growth of negatively buoyant phytoplankton

Phytoplankton population dynamics are controlled by the relative rather than absolute timescales of mixing, growth, and loss processes such as sedimentation, grazing, and so on. Here, the vertical distribution and biomass of phytoplankton populations are quantified by two timescale ratios: the Peclet number Pe—the ratio of mixing and sedimentation timescales—and the growth number G—the ratio of sedimentation and net growth timescales. Three mixing regimes are defined for phytoplankton and other particles. For Pe $ 100, the population is translated linearly down the water column over time and will leave the surface mixing layer completely after sedimentation time ts. For 0.1 , Pe , 100, the population distribution depends on the relative magnitude of Pe and G. Finally, for Pe # 0.1, the population will be vertically uniform, and biomass changes exponentially over time with characteristic timescale tc 5 ts /(G 2 1). This analysis is valid for negatively buoyant phytoplankton, except when mixing time is much longer than growth time and Pe # 0.1, which can occur for very slow sinking species. These regimes can be used for assessing the effect of changes in the mixing, growth, or sedimentation conditions on population dynamics. Published data from a lake and diurnally stratified river weir pool are used here to verify a minimum thermocline depth hypothesis proposed by others. Mixing and growth regimes are used to calculate minimum mixing depth hmin and to determine phytoplankton sinking rates from published sediment trap data. The interaction between turbulent mixing and sedimentation determines the vertical distribution of negatively buoyant phytoplankton populations (Humphries and Lyne 1988; Ruiz et al. 1996; Reynolds 1998), which in turn affects resource availability and hence phytoplankton growth (Sverdrup 1953; Reynolds 1984; Walsby 1997; Huisman et al. 2002a). A population will not grow over time unless gross production exceeds all losses, including sedimentation, which is the focus of this paper. Hence, a population of negatively buoyant phytoplankton will not grow unless the growth number, G, given by the ratio of the sedimentation timescale to the net growth timescale, exceeds unity (Condie and Bormans 1997). If mixing is ‘‘too shallow,’’ the population is limited by sedimentation losses (Visser et al. 1996b; Condie and Bormans 1997; Huisman and Sommeijer 2002b), and if mixing is ‘‘too deep,’’ the population is limited by respiration and other losses (Sverdrup 1953; Smetacek and Passow 1990; Huisman et al. 2002a). The one-dimensional form of the reaction-advection-diffusion equation quantifies the effect of sedimentation losses, 1 Present address: Department of Environmental Engineering, University of Queensland, St Lucia, Queensland, 4072, Australia. 2 Present address: Department of Biological Sciences, University of Waikato, Private Bag 3105, Hamilton, New Zealand.