Adele L. Igel | Searcharxiv

arXiv2025

Numerical Assessment of Advective and Diffusive Dynamics of Interacting and Isolated Prototypical Convectively Initiated Circulations

The bulk circulation associated with convective clouds includes not only a region of updraft and cloudy air but also a region of compensating descent and cloud-free air and horizontal motions coupling these regions. The Kinematic Representation of Non-rotating Updraft Tori (KRoNUT) model is a simple representation of this entire flow. First, the skill of the KRoNUT in representing flows from a high resolution full-physics simulation of marine tropical convection is compared to various plume representations of convection. Then the KRoNUT is used to construct bulk descriptions of the dry dynamics of isolated and interacting convective circulations under the influence of advection and diffusion (only). Cross sections of advective and diffusive tendencies show that while vertical advection of the vertical wind is the most important advective tendency in clouds, the horizontal component of the convective circulation and advection thereof plays a crucial role in the evolution of circulations in the absence of buoyancy. Strong curvature of the flow near the surface and near the updraft core results in locally strong diffusive tendencies that depend on scale. Cross sections of tendencies from the KRoNUT compare favourably to results from the simulation. Interacting circulations are shown to exhibit a wide range of dynamics with some cases of interactions leading to unique stability of geometric properties of otherwise evolving flows and some leading to geometric clustering of circulation centers.

physics.ao-ph↗

arXiv2025

Adaptive time-stepping for the Super-Droplet Method Monte Carlo collision-coalescence scheme

We present an analysis of an adaptive time-stepping scheme for the Super-Droplet Method (SDM), a Monte Carlo algorithm for simulating particle coagulation. SDM represents cloud droplets as weighted superdroplets, enabling high-fidelity representations of microphysical processes such as collision-coalescence. However, the algorithm can undercount collisions when the expected number of events is not realizable given the superdroplet configuration, introducing a biased error referred here as the collision deficit. While SDM exhibits statistical spread inherent to Monte Carlo schemes, the deficit is a systematic underestimation of collision events. This error can be addressed with adaptive time-stepping, which dynamically adjusts simulation time steps to eliminate this deficit. We analyze the behavior of the deficit across a wide range of timesteps, superdroplet counts, and initialization strategies, and explore trade-offs between accuracy and efficiency. Using the classical Safranov-Golovin test case, we show that the deficit increases with timestep and superdroplet count, and that adaptive time-stepping effectively removes the associated error without significant cost. We test a smooth continuum of initial distributions with extrema representing two different initialization methods, and find that while the deficit is sensitive to the choice of attribute-space sampling strategies, adaptive time-stepping substantially reduces the difference, allowing for users to choose initialization methods optimized for other processes. We also propose a method of visualization, capturing both the attribute sampling, droplet interactions over multiple timesteps, and the deficit using network connectivity graphs. In 2-D flow-coupled simulations, we find the deficit can have a stronger effect on convergence than previously shown, with uncorrected deficit delaying the onset of precipitation.

physics.ao-ph↗