Recipe for 1-D Lagrangian particle tracking models in space-varying diffusivity

We present a simple recipe to design a physically realistic and robust Lagrangian particle tracking model, paying particular attention to the pitfalls that are associated with the particle tracking if the turbulent mixing is taken as spatially nonuniform. These pitfalls are often neglected or ignored in Lagrangian biophysical particle tracking models and, using simple examples, it is shown how this may lead to physically and hence biologically unrealistic results. Issues associated with the direct particle tracking process are discussed. The choice of a suitable random walk model, in conjunction with an adequate random number generator, is discussed. Two methods are described to correctly implement the reflecting boundary condition in the random walk model, to avoid artificial accumulations at the boundaries. We also examine the more general question of whether the particle diffusivity can be assumed to equal the fluid diffusivity and briefly address the post-simulation treatment of the data.