Modelling of Snow Particle Settling Dynamics in Boundary Layer Turbulence: Evaluating Maxey-Riley and Reduced-Order Models with Nonlinear Drag

Abstract

Accurately modelling snow particle settling dynamics in the atmospheric boundary layer remains a fundamental challenge. These dynamics influence snowfall transport and ground snow accumulation which in turn impact hydrology, weather predictions, and climate modelling. While the foundational work of Maxey and Riley (1983), which introduced equations describing inertial particles in a fluid flow, has been used widely, the original formulation assumes linear drag and can suffer from numerical stiffness and instabilities. To gain computational efficiency and more accurately represent the settling behaviour of snow particles, this study incorporates a nonlinear drag formulation into the original Maxey-Riley equations and derives a corresponding Reduced-Order model based on perturbation theory and nonlinear dynamical system tools.

The results showed that the nonlinear Maxey-Riley model successfully reproduces key inertial particle behaviours observed in previous studies, such as loitering and sweeping. For the cases considered, vertical flow structures were found to be the primary driver of these behaviours rather than nonlinear drag alone. The Reduced-Order model replicates these hallmark features with a significant reduction in computational cost, from 24 hours to 20 minutes, while remaining numerically stable. Even though the Reduced-Order model deviates from the Maxey-Riley for larger particles, the agreement improves significantly when using model-specific terminal velocities. This highlights the Reduced-Order model's potential to capture inertial particle behaviour in atmospheric turbulence, even in its simplified form.