Phytoplankton-zooplankton dynamics in three-dimensional turbulent flows behind an idealized island

Plankton constitutes the productive base of aquatic ecosystems and plays a key role in climate dynamics, by taking part in the global carbon budget. Understanding how turbulent flows affect the distributions of planktonic species is a complex problem that has attracted considerable interest in the past, with particular emphasis on the scaling behavior of plankton variance spectra. The issue is relevant to assess the relative importance of fluid and biological dynamics, and to quantify the patchiness of plankton spatial distributions. Indeed, were the spectra of the, reactive, planktonic fields different from those of a passive (non-reactive) scalar, this would point to predominant biological activity in the corresponding range of scales. Furthermore, spectral slopes give information on the scale-by-scale intensity of the fluctuations of biological population densities and, hence, could allow to quantify the typical size of structures of highest plankton concentration.

Previous numerical studies provided interesting insight into plankton bloom formation and patchiness. However, they relied on simplified kinematic flow settings or on turbulence parametrizations. By means of direct numerical simulations, in this work we investigate the dynamics of interacting phytoplankton and zooplankton populations in two and three-dimensional turbulent wakes behind a cylinder. We mainly aim at identifying the minimal flow ingredients needed to sustain a bloom, and at characterizing how the latter could be affected by multiscale fluid properties. Notwithstanding its idealized character, the system we consider allows us to avoid any bias possibly coming from the modeling of small-scale fluid motions. Our analysis focuses on the impact of the space dimensionality of the advecting velocity field on the variance spectra, and spatial distributions, of the planktonic species.

In spite of the different statistical properties of the two-dimensional and three-dimensional carrying flows, we find that the qualitative biological dynamics in the two cases share important common features, mostly independent of the space dimensionality. This observation suggests that, in both cases, the emergence of persistent blooms is controlled by the ratio between the typical timescales of the biological activity, and of the fluid flow at large length scales. Similarly, in both two and three dimensions, we find that the spectral properties of the planktonic populations are essentially indistinguishable from those of an inert tracer. This result then hints at the prevailing role of turbulent transport over biological mechanisms in the generation of plankton patchiness. The main difference, instead, that arises from the comparison of our two and three-dimensional configurations concerns the local spatial distribution of plankton density fields. In fact, the three-dimensional turbulent dynamics tend to destroy the localized coherent structures characterizing the two-dimensional flow, in which the planktonic species are mostly concentrated, thus reducing the phytoplankton average biomass in the system.