Tidal MixingTidal ExchangeDilution of Pollutant ParticlesEnsemble Dispersion3D Exchange Tidal Mixing: An Introduction Oceanic and estuarine mixing processes have serious impacts on water quality. Tidal action and winds constantly stir the aquatic environment and the resulting degree of turbulent mixing controls transport pathways of pollutants and other particulate matter. The import or export of material in and out of aquatic systems is also modulated by tidal mixing. Lagrangian particle methods with statistically significant number of particles come as naturally suited set of tools to investigate the mixing processes in such ecosystems. Here we present estuarine and oceanic applications to provide a vision on how particles can be used in addressing natural mixing phenomena. Tidal exchange A 2005 paper entitled “Estuary/Ocean Exchange and Tidal Mixing in a Gulf of Maine Estuary: A Lagrangian Modeling Study” made an attempt to investigate how particle methods could be used to address research questions such as turbulent mixing/exchange properties, residence times and their dependency on simulation parameters in estuaries. The Great Bay Estuary in New Hampshire is used as the simulation domain. At the time, advances in computer and software technology were just beginning to allow a statistically significant number of particles to be launched on parallel processors within reasonable run times. The representative animations shown here used approximately 635,000 particles simulated using 16 processors. The passive particles were tracked for 31 days. The effects of the release time, spring-neap cycle, riverine discharge and diffusion strength on the intra-estuary and estuary-ocean exchange were investigated. Results showed the potential of first-order Markov Chain approaches in understanding estuarine mixing and exchange processes, an expected result since these are inherently Lagrangian concepts and are best treated as such. The details of this work can be found here. Estimate of the spatially variable residence time for the Great Bay estuary. The residence time is defined as the time it takes for a specific region to flush. A moving box filter is applied to average out noisiness. The color bar gives residence time in M2 tidal cycles. This is a one-month long animation of all particles used in the simulation. Note that they are color coded according to their initial starting region. The animation shows particles mixing, being exported out of the estuary and joining the Gulf of Maine coastal current under the combined effect of advection and dispersion. Same as to the left but showing only particles that originate in the uppermost section of the estuary. Same as to the left but showing only particles that originate in the coastal ocean. Dilution of Pollutant Particles A paper entitled “Dredging for Dilution: A Simulation Based Case Study in a Tidal River” investigated the real-world problem of dilution of pollutant particles originating from a wastewater treatment facility in a shallow tidal river. Dilution ratios were simulated for various bottom configuration scenarios to investigate if effective dilution can be acquired through outfall location and channel dredging. The number of dispersive particles released at each time step was specified so that there was a total of 16,000 particles at the end of the M2 tidal period long simulation. AR0 type uncorrelated random walk was used to statistically simulate turbulent dispersion. Depth averaged concentration fields and resulting dilution ratios were then generated using a simple, fixed mesh projection method in tidal time. Results, which were confirmed by Eulerian residuals, showed that the relocation of the outfall to the deeper main channel is required to reach allowed dilution ratios. This is a good example of how particle methods can help provide solutions to management communities in time and budget constrained decision making through case-oriented local applications, while increasing our understanding of natural processes and how they should be simulated at the same time. Comparison between the baseline and dredged cases showing higher particle concentrations in the vicinity of the outfall before dredging. The animation is given below. This animation shows the depth integrated concentration fields as they are before (upper frame) and after dredging (lower frame). The color bar shows concentrations and it is clipped at a maximum of 0.1 particles /m2 to emphasize smaller values (The maximum is 0.169 particles/m2). This is the animation of the dilution improvement ratio (defined as the ratio of the particle concentrations before and after dredging) in tidal time. Color bar shows the dilution ratio. Cooler colors and warmer colors show reduced (unwanted) and increased (wanted) dilution respectively. A dilution ratio of 1 ( green) means that there is no change in particle concentrations before and after dredging. This animation is the 2-color version of the dilution improvement ratio. It brings a more simplistic “yes or no” approach for a quicker qualitative check. Anything red shows increased (wanted) and anything blue shows decreased (unwanted) dilution. Ensemble Dispersion on Georges Bank A paper entitled “Modeling Turbulent Dispersion on the North Flank of Georges Bank using Lagrangian Particle Methods” investigated the circulation and transport using a data-assimilative 3-D model of frontal dynamics under stratified, tidally energetic conditions over steep topography. The contribution of tidal-time motion to the dispersion of a passive tracer was assessed using an ensemble of passive particles, simulating an at-sea dye injection in the pycnocline. 10,000 particles were released at the pycnocline at 20m and tracked for 4 days over a bathymetric depth of approximately 130m. The vertical dispersion was modeled as a random walk process sensitive to local eddy diffusivity and its gradient. There was no horizontal dispersion. The skill metric was separation rates between the centers of mass of observed (dye) and simulated ensembles. The animations here show simulations of vertically and horizontally integrated ensemble distribution in the forecast (predicted winds) and hindcast (measured winds) modes. There are no other differences among simulations. The forecast mode shows engagement in the mixing front that occurs as a result of Ekman drift from an erroneous high wind prediction. In the hindcast, observed calm winds leave the ensemble compact with no separation, a situation closer to truth as skill dictates. Snapshots of ensemble distributions in the hindcast mode. Horizontal ensemble distribution in the forecast mode. The thick blue line marks the mixing front. Isobaths are 50, 100, 150, 200m. Also shown is the wind stress [Pa] in the upper left corner. Vertical (cross-bank) ensemble distribution in the forecast mode. Horizontal ensemble distribution in the hindcast mode. The thick blue line marks the mixing front. Isobaths are 50, 100, 150, 200m. Also shown is the wind stress [Pa] in the upper left corner. Vertical (cross-bank) ensemble distribution in the hindcast mode. Forecast ensemble centers and observed tracer dye center. Markers indicate the time of observation of dye center. Hindcast ensemble centers and observed tracer dye center. Markers indicate the time of observation of dye center. Note better along-bank tracking compared to the forecast mode. 3D Exchange The Sable Gully is an underwater canyon located in the vicinity of Sable Island on the Scotian Shelf. It was designated as a Marine Protected Area (MPA) in 2004 due to many marine species living there, including the endangered northern bottlenose whale (Hyperoodon ampullatus). A 2014 paper entitled “Modelling Study of Three-Dimensional Circulation and Particle Movement over the Sable Gully of Nova Scotia” by Shan et al. investigated the circulation patterns and particle pathways at the gulley in order to provide a better understanding of the physical environment for sustainable management. The advecting and random walking particles were used in the model to study the overall pathways, downstream/upstream areas and the residence time. 3,348 color-coded particles 500m apart were launched at 200m and tracked in forward and backward time (30 days) to identify sink and source areas respectively. The release depth of 200m was based on Sable Gulley MPA vertical management zone division scheme. The tracking results predicted a gulley e-folding residence time of 7 and 13 days in February and August 2006. The flanks were high retention areas with corresponding residence times of 10 and 20 days. Results also showed that tidal circulation considerably reduces the value of residence time along the flanks. We thank Shiliang Shan of Fisheries and Oceans Canada at the Bedford Institute of Oceanography for providing the animations. The forward simulation to answer the question “Where do things go?”. Particles were released at 200m (center panel). The left panel shows particles that traveled above 180m; the center panel shows particles that stayed between 180 and 220m. The right panel shows particles that moved below 220m. The backward simulation to answer the question “Where do things come from?”. Everything else is similar to the forward animation on the left.