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

TLDR

Direct particle tracking in heterogeneous turbulence requires careful selection of random walk models and random number generators to avoid methodological pitfalls. The study offers a practical recipe for building robust Lagrangian particle tracking models that explicitly address pitfalls of spatially varying turbulence and examine whether particle diffusivity equals fluid diffusivity. The authors present a simple, step‑by‑step recipe that includes illustrative examples, two techniques for correctly implementing reflecting boundary conditions, and guidance on post‑simulation data handling. The work demonstrates that neglecting these pitfalls can produce physically and biologically unrealistic outcomes.

Abstract

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.