Small-scale turbulence in the plankton: low-order deterministic chaos or high-order stochasticity?

Almost all regions of the oceans are heavily influenced by the effects of physical processes such as turbulence which in turn influence the distribution and ecology of organisms that occupy these regions. There is a real need for additional focus placed on the precise knowledge of both physical and biological processes which is often difficult using basic time series analysis. In that way, we applied nonlinear analysis techniques to high frequency time series of temperature, salinity and phytoplankton concentrations recorded in different hydrodynamical regimes related to tidal forcing in a tidally mixed coastal ecosystem. Techniques devoted to the identification of low-order deterministic chaos cannot find evidence of chaos. While a lower dimensionality was identified in low hydrodynamic conditions, the results rather suggest stochastic time series with many degrees of freedom: no obvious attractor in phase space trajectory, LLE indistinguishable from zero, absence of convergence of the correlation integral. We then applied to these data specific multifractal analysis techniques and showed that these time series clearly exhibit high-order stochasticity. In addition, the stochastic structure of purely passive scalars (i.e., temperature and salinity) remained invariant, while the one of phytoplankton biomass must be regarded as highly structured in time by both hydrodynamic and advective processes.