Persistence of cluster synchronization under the influence of advection

We present a study on the emergence of spatial structure in plankton dynamics under the influence of stirring and mixing. A distribution of plankton is represented as a lattice of nonidentical, interacting, oscillatory plankton populations. Each population evolves according to (i) the internal biological dynamics represented by an NPZ model with population-specific phytoplankton growth rate, (ii) sub-grid-cell stirring and mixing parameterized by a nearest-neighbor coupling, and (iii) explicit advection resulting from a constant horizontal shear. Using the methods of synchronization theory, the emergent spatial structure of the simulation is investigated as a function of the coupling strength and rate of advection. Previous work using similar methods has neglected the effects of explicit stirring (i.e., at scales larger than the grid cell), leaving as an open question the relevance of the work to real marine systems. Here, we show that persistent spatial structure emerges for a range of coupling strengths for all realistic levels of surface ocean shear. Spatially, this corresponds to the formation of temporally evolving clusters of local synchronization. Increasing shear alters the spatial characteristics of this clustering by stretching and narrowing patches of synchronized dynamics. These patches are not stretched into stripes of synchronized abundance aligned with the flow, as may be expected, but instead lie at an angle to the flow. This study shows that advection does not diminish the relevance of conclusions from previous studies of spatial structure in plankton simulations. In fact, the inclusion of advection adds characteristic filamental structure, as observed in real-world plankton distributions. The results also show that the ability of coupled oscillators to synchronize depends strongly on the spatial arrangement of oscillator natural frequencies; under the influence of advection, therefore, the impact of the coupling strength on the emergent spatial structure of a biophysical simulation is time-dependent.