Numerical simulations of the competition between wind-driven mixing and surface heating in triggering spring phytoplankton blooms

About 60 years ago, Sverdrup formalized the critical depth hypothesis to explain the timing of the spring phytoplankton bloom in terms of the depth of the surface mixed layer. In recent years, a number of refinements and alternatives to the critical depth hypothesis have been proposed, including the critical turbulence hypothesis which states that a bloom can occur when turbulent mixing is sufficiently weak, irrespective of the mixed layer depth. Here, we examine the relative influence of wind-driven mixing and net surface heating on phytoplankton growth. Of particular interest is whether wind-driven mixing can delay the spring bloom after winter convection gives way to net surface warming. We address these questions using high-resolution large-eddy simulations (LES) coupled with a simple phytoplankton model. We also describe an analytical phytoplankton model with a formulation for the turbulent mixing based on the LES results. For a constant, prescribed surface heat flux, net phytoplankton growth is seen when the windstress is smaller than a critical value. Similarly, for a constant windstress, a critical heat flux separates cases with growing and decaying phytoplankton populations. Using the LES results, we characterize the critical windstress and critical heat flux in terms of other physical and biological parameters and propose a simple expression for each based on the analysis of the analytical model. Phytoplankton growth begins when the mixing depth shoals above the critical depth, consistent with the critical depth hypothesis. Our results provide a framework to interpret blooms in other conditions where both the depth and the intensity of turbulent mixing might be crucial factors in influencing phytoplankton growth.