Lateral stirring is a basic oceanographic phenomenon affecting the distribution of physical, chemical, and biological fields. Eddy stirring at scales on the order of 100 km (the mesoscale) is fairly well understood and explicitly represented in modern eddy-resolving numerical models of global ocean circulation. The same cannot be said for smaller-scale stirring processes. Here, the authors describe a major oceanographic field experiment aimed at observing and understanding the processes responsible for stirring at scales of 0.1–10 km. Stirring processes of varying intensity were studied in the Sargasso Sea eddy field approximately 250 km southeast of Cape Hatteras. Lateral variability of water-mass properties, the distribution of microscale turbulence, and the evolution of several patches of inert dye were studied with an array of shipboard, autonomous, and airborne instruments. Observations were made at two sites, characterized by weak and moderate background mesoscale straining, to contrast different regimes of lateral stirring. Analyses to date suggest that, in both cases, the lateral dispersion of natural and deliberately released tracers was O(1) m2 s–1 as found elsewhere, which is faster than might be expected from traditional shear dispersion by persistent mesoscale flow and linear internal waves. These findings point to the possible importance of kilometer-scale stirring by submesoscale eddies and nonlinear internal-wave processes or the need to modify the traditional shear-dispersion paradigm to include higher-order effects. A unique aspect of the Scalable Lateral Mixing and Coherent Turbulence (LatMix) field experiment is the combination of direct measurements of dye dispersion with the concurrent multiscale hydrographic and turbulence observations, enabling evaluation of the underlying mechanisms responsible for the observed dispersion at a new level.

We derive a closed master equation for an individual-based population model in continuous space and time. The model and master equation include Brownian motion, reproduction via binary fission, and an interaction-dependent death rate moderated by a competition kernel. Using simulations we compare this individual-based model with the simplest approximation, the spatial logistic equation. In the limit of strong diffusion the spatial logistic equation is a good approximation to the model. However, in the limit of weak diffusion the spatial logistic equation is inaccurate because of spontaneous clustering driven by reproduction. The weak-diffusion limit can be partially analyzed using an exact solution of the master equation applicable to a competition kernel with infinite range. This analysis shows that in the case of a top-hat kernel, reducing the diffusion can increase the total population. For a Gaussian kernel, reduced diffusion invariably reduces the total population. These theoretical results are confirmed by simulation. r

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The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a survival-extinction transition; the location of this transition in the parameter space is constrained using variational arguments and delimited by simulations. The statistical steady state reached when the system is in the survival region of parameter space is characterized by integral constraints and upper and lower bounds on the biomass and productivity that follow from variational arguments and direct inequalities. In the limit of zero-decorrelation time the velocity field is shown to act as Fickian diffusion with an eddy diffusivity much larger than the molecular diffusivity and this allows a one-dimensional model to predict the biomass, productivity and extinction transitions. All results are illustrated with a simple growth and stirring model.

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