Adaptive stochastic trajectory modelling of transport in geophysical flows
Seminar Room 1, Newton Institute
AbstractMotivated by the goal of improving and augmenting stochastic Lagrangian models of particle dispersion in turbulent geophysical flows, techniques from the theory of stochastic processes are applied to a model transport problem. The aim is to find an efficient and accurate method to calculate the total tracer transport between a source and a receptor when the flow between the two locations is weak, rendering direct stochastic Lagrangian simulation prohibitively expensive. Two methods are found to be useful. The first is Milstein's `measure transformation method', which involves adding an artificial velocity to the trajectory equation, and simultaneously correcting for the weighting given to each particle under the new flow. Various difficulties associated with making an appropriate choice for the artificial velocity field are detailed and addressed. The second method is a variant of Grassberger's `go-with-the-winners' branching process, which acts to remove particles unlikely to contribute to the net transport, and reproduces those that will contribute. A simple solution to the problem of defining a `winner' for flows in a high Peclet number chaotic advection regime is proposed. It is demonstrated that, used independently or together, the two methods can act to reduce the variance of estimators of the total transport by several orders of magnitude compared with direct simulation.
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