Sufficient noise and turbulence can induce phytoplankton patchiness

Phytoplankton patchiness ubiquitously observed in marine ecosystems is a simple physical phenomenon. Only two factors are required for its formation: one is persistent variations of inhomogeneous distributions in the phytoplankton population and the other is turbulent stirring by eddies. It is not necessary to assume continuous oscillations such as limit cycles for realization of the first factor. Instead, a certain amount of noise is enough. Random fluctuations by environmental noise and turbulent advection by eddies seem to be common in open oceans. Based on these hypotheses, we propose seemingly the simplest method to simulate patchiness formation that can create realistic images. Sufficient noise and turbulence can induce patchiness formation even though the system lies on the stable equilibrium conditions. We tentatively adopt the two-component model with nutrients and phytoplankton, however, the choice of the mathematical model is not essential. The simulation method proposed in this study can be applied to whatever model with stable equilibrium states including one-component ones.