Results are presented from two dye release experiments conducted in the seasonal thermocline of the Sargasso Sea, one in a region of low horizontal strain rate (10(-6) s(-1)), the second in a region of intermediate horizontal strain rate (10(-5) s(-1)). Both experiments lasted 6 days, covering spatial scales of 1-10 and 1-50 km for the low and intermediate strain rate regimes, respectively. Diapycnal diffusivities estimated from the two experiments were kappa(z) = (2-5) x 10(-6) m(2) s(-1), while isopycnal diffusivities were kappa(H) = (0.2-3) m(2) s(-1), with the range in kappa(H) being less a reflection of site-to-site variability, and more due to uncertainties in the background strain rate acting on the patch combined with uncertain time dependence. The Site I (low strain) experiment exhibited minimal stretching, elongating to approximately 10 km over 6 days while maintaining a width of 5 km, and with a notable vertical tilt in the meridional direction. By contrast, the Site II (intermediate strain) experiment exhibited significant stretching, elongating to more than 50 km in length and advecting more than 150 km while still maintaining a width of order 3-5 km. Early surveys from both experiments showed patchy distributions indicative of small-scale stirring at scales of order a few hundred meters. Later surveys show relatively smooth, coherent distributions with only occasional patchiness, suggestive of a diffusive rather than stirring process at the scales of the now larger patches. Together the two experiments provide important clues as to the rates and underlying processes driving diapycnal and isopycnal mixing at these scales.

by Andrey y. ShcherbinA, MileS A. SunderMeyer, eric Kunze, eric d’ASAro, GuAltiero bAdin, dAniel birch, Anne-MArie e. G. brunner-SuzuKi, Jörn cAllieS, brAndy t. Kuebel cervAnteS, MArionA clAret, briAn concAnnon, Jeffrey eArly, rAffAele ferrAri, louiS GoodMAn, rAMSey r. hArcourt, Jody M. KlyMAK, crAiG M. lee, M.-PAScAle lelonG, MurrAy d. levine, ren-chieh lien, AMAlA MAhAdevAn, JAMeS c. McWilliAMS, M. Jeroen MoleMAKer, SonAlJit MuKherJee, JonAthAn d. nASh, tAMAy özGöKMen, StePhen d. Pierce, SAnJiv rAMAchAndrAn, roGer M. SAMelSon, thoMAS b. SAnford, r. KiPP SheArMAn, eric d. SKyllinGStAd, K. ShAfer SMith, AMit tAndon, John r. tAylor, euGene A. terrAy, leif n. thoMAS, And JAMeS r. ledWell

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) m(2) 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.

Two near-surface dye releases were mapped on scales of minutes to hours temporally, meters to order 1 km horizontally, and 1-20 m vertically using a scanning, depth-resolving airborne lidar. In both cases, dye evolved into a series of rolls with their major axes approximately aligned with the wind and/or near-surface current. In both cases, roll spacing was also of order 5-10 times the mixed layer depth, considerably larger than the 1-2 aspect ratio expected for Langmuir cells. Numerical large-eddy simulations under similar forcing showed similar features, even without Stokes drift forcing. In one case, inertial shear driven by light winds induced large aspect ratio large-eddy circulation. In the second, a preexisting lateral mixed layer density gradient provided the dominant forcing. In both cases, the growth of the large-eddy structures and the strength of the resulting dispersion were highly dependent on the type of forcing.

Breaking groups of large-amplitude internal gravity waves are simulated numerically and the resulting diapycnal mixing and residual momentum are quantified. The wave frequency strongly affects the mixing, with high- and low-frequency waves doing many times more mixing than intermediate-frequency waves with the same steepness. The total residual momentum remaining in the breaking region after the remnants of the wave group propagates away shows similar frequency dependence as the diapycnal mixing. Additionally, the propagation of the breaking events and the spatial distribution of the mixing are found to agree qualitatively with a kinematic description of breaking internal wave groups.

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We show that a steady vertically-sheared current can produce a thin layer of plankton by differentially advecting an initial patch whose vertical and horizontal dimensions are H0 and L0, respectively. Our model treats the plankton as an inert passive tracer with vertical diffusivity κv and subject to a vertically-sheared horizontal current with shear α. After a transient of duration L0/αH0 the vertical thickness H of the patch decreases with H(t)≈L0/αt. This shear-driven thinning is halted by diffusion at a time of order α-2/3κv-1/3L02/3, and at this time the layer achieves a minimum layer thickness of order α-1/3κv1/3L01/3. For typical oceanic parameters, such as κv∼10-5m2s-1, α∼10-2s-1, and L0∼1000m the initial transient is about 3h and the layer achieves a minimum thickness of order 1m in a time of order 1 day. During the shear thinning the intensity of the layer decreases by a factor of 3-1/2≈0.58, which means that the intensity of the thin layer is comparable to the intensity of the patch from which it was formed. Subsequently the layer thickens and its intensity decreases; the coup de grace is delivered by shear dispersion at a time of order H02/κv. The lifetime of the thin layer, defined by the condition that the maximum concentration is comparable to the initial maximum concentration, is the same order as the time to achieve minimum thickness. Additionally, analysis of a nutrient–phytoplankton model shows that phytoplankton growing in a sheared patch of nutrients can result in a layer of phytoplankton that develops as an initially thin feature.

The Fisher-Kolmogorov-Petrovskii-Piskunov 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: 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.

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.