Lagrangian Stochastic Modeling of the Coastal Fumigation Phenomenon

Abstract

Most coastal fumigation models utilize questionable assumptions and ignore some of the physics that play an important role in the diffusion process. The Lagrangian stochastic dispersion modeling technique has the potential for simulating the fumigation phenomenon in a more physically sound way by calculating dispersion directly in terms of flow properties, thereby providing a tool with which simpler models can be tested and developed. A two-dimensional Lagrangian stochastic model incorporating streamwise diffusion and gradients (i.e., derivatives) of flow properties in both vertical and horizontal directions is developed. The mean correlation between the streamwise and the vertical Eulerian velocities is neglected in constructing the model. The model is nondimensionalized and then applied to coastal fumigation for a number of cases involving different values of meteorological and source parameters to investigate how these parameters affect dispersion. The results reveal that the gradients of flow properties in the streamwise direction can he neglected for most fumigation situations. It is also found that the effects of streamwise diffusion are smaller for plumes having larger vertical spreads at the intersection point of the plume centerline and the coastal thermal internal boundary layer (TIBL) and can be neglected in a model for sufficiently large values of wind speed. These results suggest that the one-dimensional (vertical) version of our stochastic model, which employs Taylor's translation hypothesis and incorporates the spatial growth of the TIBL and a constant value of the convective velocity, is adequate for describing the fumigation process. This one-dimensional model, together with a Langevin model in the lateral direction, is then applied to data from the Nanticoke field experiment on fumigation conducted in the summer of 1978 in Ontario, Canada. The Nanticoke data are analysed and nondimensionalized prior to model comparison. The overall performance of the model is good. The one-dimensional model is also successfully applied to existing water-tank data, which are representative of the coastal fumigation phenomenon. The stochastic model results are compared with those from an analytical model, which assumes an instantaneous and uniform vertical mixing in the TIBL.