microflows and microscale heat transfer laboratory

​Lagrangian particle tracking technique that implements a combined Eulerian-Lagrangian approach is a tool that tracks Lagrangian particles advected using a Eulerian velocity field. This versatile modeling tool finds many applications in oceanography and has become a reliable technique that decision makers rely on in order to establish appropriate plans. However, the quest to develop accurate and efficient tracking techniques is often faced by challenges that need to be overcome. Eulerian uncertainties arising from the many velocities a particle can have at a given time step are one of those challenges. For instance, the velocity field resulting from data assimilation is an ensemble of several members generated at each assimilation cycle. This results in an exponentially increasing number of trajectories at each time step if a particle is said to follow the combinations of velocities of the previous time steps, a fact that makes unpractical tracking each individual particle.

To overcome this difficulty, binning the final positions of particles is proposed. Whenever many trajectories lead a particle to the same bin, they are regarded as a single trajectory that moves the particle to the center of that bin which will have a probability related to the number of trajectories leading that particle to it. This allows to generate probability maps that describe efficiently the dispersion of particles while managing wisely the computational cost by reducing significantly the sheer amount of growing data.

This method was applied to an oil spill problem in the Red Sea. Forward Lagrangian particle tracking was employed to simulate the propagation of the oil spill from a fixed as well as a moving source, while inverse (backward) Lagrangian particle tracking was used to specify probable sources of the spill assuming that the age of particles is provided. The model also accounts for beaching which is an important feature that allows to predict the location of the coasts with high probability of beached oil.