Stochastic Particle Models For Transport Problems In Coastal Waters
Free (open access)
W. M. Charles, A. W. Heemink & E. van den Berg
In this paper transport processes in coastal waters are described by stochastic dif-ferential equations (SDEs). These SDEs are also called particle models (PMs). By interpreting a Fokker-Planck equation associated with the SDE as an advec-tion diffusion equation (ADE), it is possible to derive the underlying PM which is exactly consistent with the ADE. Both the ADE and the related classical PM do not take into account accurately the short term spreading behaviour of particles. In the PM this shortcoming is due to the driving noise in the SDE which is mod-elled as a Brownian motion and therefore has independent increments. To improve the behaviour of the model shortly after the release of pollution we develop an improved PM forced by a coloured noise process representing the short-term cor-related turbulent velocity of the particles. This way a more accurate and detailed short-term initial spreading behaviour of particles is achieved. For long-term sim-ulations both the improved and classical PMs are consistent with the ADE. How-ever, the improved PMis relatively easier to handle numerically than a correspond-ing ADE. In this paper both models are applied to a real life pollution problem in the Dutch coastal waters. Keywords: Brownian motion, stochastic differential equations, particle models, coloured noise force, advection-diffusion equation, Fokker-Planck equation. 1 Introduction Environmental management of shallow water areas requires a clear insight in the aftermath of, for instance, ship accidents or waste disposal. A good environmental control system must have the possibility to accurately predict the dispersion of pol-lutants. Particle models, play an important role in modelling transport phenomena
Brownian motion, stochastic differential equations, particle models, coloured noise force, advection-diffusion equation, Fokker-Planck equation.