Lagrangian Particle Simulations Research Articles

Does large-scale ocean circulation structure life history connectivity in Antarctic toothfish (Dissostichus mawsoni)?

A multidisciplinary approach incorporating otolith chemistry, age data, and numerical Lagrangian particle simulations indicated a single, self-recruiting population of Antarctic toothfish (Dissostichus mawsoni) in the Southeast Pacific Basin (SPB) and Ross Sea, with a life history structured by the large-scale circulation. Chemistry deposited prior to capture along otolith edges demonstrated strong environmental heterogeneity, yet the chemistry in otolith nuclei, deposited during early life, showed no differences. Age data showed only adult fish in catches on the Pacific–Antarctic Ridge in the SPB and structuring of life stages consistent with transport pathways from the northern Ross Sea. Lagrangian particle simulations predicted that early life stages following the flow in the SPB would be transported to areas in the Ross Sea where juveniles are caught, whereas the circulation would facilitate adult movement along the shelf slope and back into the SPB where spawning adults are caught. These results suggest that successfully spawning fish spend only a part of their adult life history in the Ross Sea, areas in the eastern Ross Sea contribute disproportionately to the spawning population, and areas in the southwestern Ross Sea may supply fisheries in the southern Indian Ocean.

Asymptotic properties of wall-induced chaotic mixing in point vortex pairs

The purpose of this work is to analyze the flow due to a potential point vortex pair in the vicinity of a symmetry line (or “wall”), in order to understand why the presence of the wall, even far from the vortices, accelerates fluid mixing around the vortex pair. An asymptotic analysis, in the limit of large distances to the wall, allows to approximate the wall effect as a constant translation of the vortex pair parallel to the wall, plus a straining flow which induces a natural blinking vortex mechanism with period half the rotation period. A Melnikov analysis of lagrangian particles, in the frame translating and rotating with the vortices, shows that a homoclinic bifurcation indeed occurs, so that the various separatrices located near the vortex pair (and rotating with it) do not survive when a wall is present. The thickness of the resulting inner stochastic layer is estimated by using the separatrix map method and is shown to scale like the inverse of the squared distance to the wall. This estimation provides a lower-bound to the numerical thickness measured from either Poincaré sections or simulations of lagrangian particles transported by the exact potential velocity field in the laboratory frame. In addition, it is shown that the outer homoclinic cycle, separating the vortices from the external (open) flow, is also perturbed from inside by the rotation of the vortex pair. As a consequence, a stochastic layer is shown to exist also in the vicinity of this cycle, allowing fluid exchange between the vortices and the outer flow. However, the thickness of this outer stochastic zone is observed to be much smaller than the one of the inner stochastic zone near vortices, as soon as the distance to the wall is large enough.

Isolation by oceanographic distance explains genetic structure for Macrocystis pyrifera in the Santa Barbara Channel.

Ocean currents are expected to be the predominant environmental factor influencing the dispersal of planktonic larvae or spores; yet, their characterization as predictors of marine connectivity has been hindered by a lack of understanding of how best to use oceanographic data. We used a high-resolution oceanographic model output and Lagrangian particle simulations to derive oceanographic distances (hereafter called transport times) between sites studied for Macrocystis pyrifera genetic differentiation. We build upon the classical isolation-by-distance regression model by asking how much additional variability in genetic differentiation is explained when adding transport time as predictor. We explored the extent to which gene flow is dependent upon seasonal changes in ocean circulation. Because oceanographic transport between two sites is inherently asymmetric, we also compare the explanatory power of models using the minimum or the mean transport times. Finally, we compare the direction of connectivity as estimated by the oceanographic model and genetic assignment tests. We show that the minimum transport time had higher explanatory power than the mean transport time, revealing the importance of considering asymmetry in ocean currents when modelling gene flow. Genetic assignment tests were much less effective in determining asymmetry in gene flow. Summer-derived transport times, in particular for the month of June, which had the strongest current speed, greatest asymmetry and highest spore production, resulted in the best-fit model explaining twice the variability in genetic differentiation relative to models that use geographic distance or habitat continuity. The best overall model also included habitat continuity and explained 65% of the variation in genetic differentiation among sites.

Realized and potential larval connectivity in the Southern California Bight

Populations of many nearshore marine species are connected through the dispersal of their larvae. In this paper, larval connectivity patterns in the Southern California Bight are explored using 2 quantities: potential and realized larval connectivity. Potential connectivity is defined as the probability of larval transport from a source to a destination location and is quantified using Lagrangian particle simulations. Realized connectivity is the product of potential connectivity with larval production and can be used to estimate larval settlement patterns. Potential and realized con- nectivity patterns are quantified for kelp bass Paralabrax clathratus, kelp rockfish Sebastes atro- virens, and red abalone Haliotis rufescens, 3 species with a range of larval dispersal characteristics. Connectivity patterns were found to be both heterogeneous, with locations having different source and destination strengths, and asymmetric, with directionality in larval transport. Both potential and realized connectivity were strongly influenced by the length and timing of the spawning season as well as planktonic larval duration. For kelp bass and kelp rockfish, a strong correspondence was found between realized and potential destination locations, suggesting that circulation processes have a dominant role in shaping the spatial distribution of these 2 species. Strong temporal variabil- ity in realized larval connectivity was observed on seasonal and inter-annual time scales (particularly between El Nino and La Nina conditions). These results provide novel information for use in marine fisheries and conservation management.

A Lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue

We present a novel Lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue. Linear solids are represented by the Lagrangian formulation of the stress–strain relationship that is extended to nonlinear solids by using the Lagrangian evolution of the deformation gradient described in a moving framework. The present method introduces a level set description, along with the particles, to capture the body deformations and to enforce the boundary conditions. Furthermore, the accuracy of the method in cases of large deformations is ensured by implementing a particle remeshing procedure. The method is validated in several benchmark problems, in two and three dimensions and the results compare well with the results of respective finite elements simulations. In simulations of large solid deformation under plane strain compression, the finite element solver exhibits spurious structures that are not present in the Lagrangian particle simulations. The particle simulations are compared with experimental results in an aspiration test of liver tissue.

Mesoscale convective systems in Spain: instability conditions and moisture sources involved

Abstract. Source-receptor water vapor content areas are analyzed for a particular case of deep mesoscale convective system (MCS) developed over the Mediterranean margin of Spain in October 1982. The aim of this work is to study simultaneously the atmospheric instability conditions and water vapour fluxes which finally resulted in very severe precipitation rates, reaching up to 600 mm in a single day. Humidity amounts and transport are quantified along the trajectories computed from a lagrangian particle simulation model (FLEXPART6.2). To evaluate the precipitation probability, the water vapor content and both thermodynamic and dynamic atmospheric instability components were assessed. The October 1982 Iberian MCS occurred as a consequence of a deep cutoff low detected between 500 and 200 hPa levels. The dynamical instability was measured through potential vorticity anomalies and Q vector divergence, which presented their maximum and minimum centers respectively over south-eastern Iberia. Synoptic and dynamic instability conditions were obtained from the ERA-40 reanalysis dataset. It is observed that during this severe weather episode, the specific humidity increased along the lowest and easternmost trajectories, which are mainly spread over the Mediterranean Sea.

Lagrangian statistics of Navier–Stokes and MHD turbulence

AbstractWe report on a comparison of high-resolution numerical simulations of Lagrangian particles advected by incompressible turbulent hydro- and magnetohydrodynamic (MHD) flows. Numerical simulations were performed with up to 10243 collocation points and 10 million particles in the Navier–Stokes case and 5123 collocation points and 1 million particles in the MHD case. In the hydrodynamics case our findings compare with recent experiments from Mordant et al. (2004 New J. Phys.6, 116) and Xu et al. (2006 Phys. Rev. Lett.96, 024503). They differ from the simulations of Biferale et al. (2004 Phys. Rev. Lett.93, 064502) due to differences of the ranges chosen for evaluating the structure functions. In Navier–Stokes turbulence intermittency is stronger than predicted by the multifractal approach of Biferale et al. (2004 Phys. Rev. Lett.93, 064502) whereas in MHD turbulence the predictions from the multifractal approach are more intermittent than observed in our simulations. In addition, our simulations reveal that Lagrangian Navier–Stokes turbulence is more intermittent than MHD turbulence, whereas the situation is reversed in the Eulerian case. Those findings can not consistently be described by the multifractal modeling. The crucial point is that the geometry of the dissipative structures have different implications for Lagrangian and Eulerian intermittency. Application of the multifractal approach for the modeling of the acceleration probability density functions works well for the Navier–Stokes case but in the MHD case just the tails are well described.

Transport and retention of dormant copepods in the Gulf of Maine

Abstract Variability in the availability of dormant copepods to seed productive shelf areas has been hypothesized to influence the abundance of the dominant copepod species Calanus finmarchicus in several regions of the North Atlantic. One source of this variability is advection of dormant copepods in deep water. Using Lagrangian particle simulations, we examined the influence of environmental forcing and copepod behavior on transport and retention of dormant C. finmarchicus in the deep Gulf of Maine, in the northwestern Atlantic. Retention in the Gulf of Maine was relatively high, >40% over 6 months, under all conditions simulated. Transport within the Gulf of Maine was high, resulting in shifts of eastern copepods into the western Gulf and of upstream copepods, from slope and Scotian Shelf waters, into the eastern Gulf. Copepod behavior during dormancy was a major source of uncertainty, but it is probably not a major source of interannual variability in retention. Retention increased with the initial depth of dormant copepods, and vertical positioning behavior had a strong influence on retention for simulations started at depths greater than 150 m, because copepods that can stay below basin sill depths are retained. Mean cross-shore winds reduced retention slightly (

Recruitment variability in Baltic Sea sprat (Sprattus sprattus) is tightly coupled to temperature and transport patterns affecting the larval and early juvenile stages

Recruitment patterns of Baltic Sea sprat (Sprattus sprattus) were correlated to time series of (i) month- and depth-specific temperature conditions and (ii) larval drift patterns inferred from long-term Lagrangian particle simulations. From the latter, we derived an index that likely reflected the variable degree of annual larval transport from the central, deep spawning basins to the shallow coastal areas of the Baltic Sea. The drift index was significantly (P < 0.001) correlated to sprat recruitment success and explained, together with sprat spawning stock biomass, 82% of the overall variability between 1979 and 2003. Years of strong larval displacement towards southern and eastern Baltic coasts corresponded to relative recruitment failure, while years of retention within the deep basins were associated with relative recruitment success. The strongest correlation between temperature and recruitment occurred during August in surface waters, explaining 73% of the overall variability. Together, the two approaches advocate that new year classes of Baltic sprat are predominantly composed of individuals born late in the season and are determined in strength mainly by processes acting during the late larval and early juvenile stages. However, prior to be included in recruitment predictions, the biological mechanisms underlying these strong correlations may need to be better resolved.

Linking growth to environmental histories in central Baltic young‐of‐the‐year sprat, Sprattus sprattus: an approach based on otolith microstructure analysis and hydrodynamic modelling

AbstractOtolith microstructure analysis and hydrodynamic modelling were combined to study growth patterns in young‐of‐the‐year (YoY) sprat, Sprattus sprattus, which were sampled in October 2002 in the central Baltic Sea. The observed ‘window of survival’, approximated by the distribution of back‐calculated days of first feeding (DFF), was narrow compared to the extended spawning season of sprat in the Baltic Sea (mean± SD = 22 June ± 14.1 days) and indicated that only individuals born in summer survived until October 2002. Within the group of survivors, individuals born later in the season exhibited faster larval, but more rapidly decreasing juvenile growth rates than earlier born conspecifics. Back‐calculated larval growth rates of survivors (0.48–0.69 mm day−1) were notably higher than those previously reported for average larval sprat populations, suggesting that the YoY population was predominantly comprised of individuals which grew faster during the larval stage. Daily mean temperatures, experienced across the entire YoY population, were derived from Lagrangian particle simulations and correlated with (1) detrended otolith growth and (2) back‐calculated, daily somatic growth rates of survivors. The results showed that abrupt changes in ambient temperature can be detected in the seasonal pattern of otolith growth, and that higher temperatures led to significantly faster growth throughout the entire age range of YoY sprat.

Shear viscosity of bulk suspensions at low Reynolds number with the three-dimensional lattice Boltzmann method

We report three-dimensional parallel Lagrangian particle simulations using the lattice Boltzmann method, conducted at a low Reynolds number. Using modified Lees-Edwards boundary conditions and directly calculated viscous dissipation, we show that it is possible to recover excellent agreement with the Einstein viscosity formula in the low concentration limit and to predict viscosity corrections for larger concentrations.

Dependence of fragmentation behavior of colloidal aggregates on their fractal structure

The fragmentation dynamics of aggregate of non-Brownian particles in shear flow is investigated numerically. The breakup behaviors of aggregates having the same connectivity but the different space-filling properties are examined. The Lagrangian particle simulation in a linear flow field is performed. The effect of surrounding fluid on the motion of multiple particles is estimated by Stokesian dynamics approach. The inter-particle force is calculated from the retarded van der Waals potential based on the Lifshitz theory. The results obtained in this work indicate that the fragmentation behavior of colloidal aggregates depends on their fractal structure. However, if the resultant aggregate size is smaller than the critical one, the fragmentation behavior shows the universality regardless of their original structure. Furthermore, the restructuring of aggregate in shear flow and its effect on the fragmentation process are also discussed.

Comparison between Lagrangian and Eulerian particle simulations coupled with DNS of homogeneous isotropic decaying turbulence

Comparison between Lagrangian and Eulerian particle simulations coupled with DNS of homogeneous isotropic decaying turbulence

Lateral mixing and the North Atlantic Tracer Release Experiment: Observations and numerical simulations of Lagrangian particles and a passive tracer

Mixing and stirring of Lagrangian particles and a passive tracer were studied by comparison of float and tracer observations from the North Atlantic Tracer Release Experiment (NATRE). Statistics computed from the NATRE floats were found to be similar to those estimated by Ledwell et al. [this issue] from the tracer dispersion. Mean velocities computed from the floats were cm/s for the (zonal, meridional) components, and large‐scale effective eddy diffusivities were (κe11, κe22) = (1.5±0.7, 0.7±0.4) × 103 m2/s. The NATRE observations were used to evaluate theoretical models of tracer and particle dispersal. The tracer dispersion observed by Ledwell et al. [this issue] was consistent with an exponential growth phase for about the first 6 months and a linear growth at larger times. A numerical model of mesoscale turbulence that was calibrated with float statistics also showed an exponential growth phase of tracer and a reduced growth for longer times. Numerical results further show that Garrett's [1983] theory, relating the effective small‐scale diffusivity to the rms strain rate and tracer streak width, requires a scale factor of 2 when the observed growth rate of streak length is used as a measure of the strain rate. This scale factor will be different for different measures of the strain rate and may also be affected by temporal and spatial variations in the mesoscale strain field.

Passive scalar diffusion from surface sources in the convective boundary layer

We examine vertical and horizontal diffusion of a passive scalar puff from a surface point source in a convective boundary layer (CBL). Numerical results are presented from a large-eddy simulation (LES) with embedded subgrid Lagrangian particle simulation (LPS). There is good agreement in most respects with previous laboratory and numerical studies. Analytical approximations for the concentration, horizontal flux and vertical flux are found to work reasonably well; they are based on the assumption that the concentration follows a Gaussian function in the horizontal and vertical, and that the dimensionless width and height scales of the puff follow simple functions of time. Fluxes and concentration gradients are related through a continuity relationship, without the need for an eddy diffusivity assumption. The instantaneous, point-source fields can be integrated for any source geometry. We compare predictions from the LES/LPS model for a sinusoidal surface flux with previous results from an LES with sinusoidal buoyancy flux and confirm that the buoyancy perturbations diffuse like a passive scalar. We also consider a continuous point source and derive footprint functions for vertical flux measurements above the surface layer.

Lagrangian Particle Simulation of Tracer Dispersion in the Lee of a Schematic Two-Dimensional Hill

Abstract Spray, a 3D Lagrangian particle model for the simulation of complex flow dispersion, is presented. Its performance is tested against the Environmental Protection Agency wind tunnel concentration distribution of passive tracer released from elevated point sources, located in the lee region of a two-dimensional schematic hill, in a neutrally stratified boundary layer. Based on the measured values of the first two moments of the turbulent flow velocity, the mean fields are computed over a regular grid using a mass-consistent model, whereas the turbulence structure is simply interpolated. From these fields, trajectories of tracer particles are computed using a linear formulation of the Langevin equation, with a correlated, skewed forcing. The self-consistence test (well-mixed condition), aimed at maintaining an initially well-mixed particle distribution uniform in time, has shown satisfactory results in the region under study. The computed concentration field turns out to be in good agreement with th...

A tight package wrapping for planar point-sets

Three algorithms for generating the convex hull of a discrete point-set in the plane are extended to a non-convex wrapping to follow concavities in the points distributions. Complexity of computation is derived along with actual performance on generated data sets of varying cardinalities. Some postulated anomalies are removed, with examples. Two real-life examples of the use of the algorithms are presented: a Lagrangian particle simulation of a pollutant plume on the surface of a large lake, and a visualization of a two-dimensional point-set of water quality data showing the population of anion-cation pairs of observations of lakes and rivers for various tertiary watersheds in Eastern Canada.