Modal analysis reveals imprint of snowflake shape on wake flow structures

Abstract

This study investigates the complex interplay of wake flow dynamics, particle shape, and falling behavior of snowflakes through advanced flow analysis. We employ Proper Orthogonal Decomposition and Dynamic Mode Decomposition to analyze the wake flow patterns of three distinct snowflake geometries at a Reynolds number of 1500: a dendrite crystal, a columnar crystal, and a rosette-like particle. Proper Orthogonal Decomposition reveals that spatial resolution significantly impacts the capture of flow structures, particularly for particles with more intricate wake flow structure, corresponding to unstable falling motion. Dynamic Mode Decomposition demonstrates high sensitivity to temporal resolution, with data of the forces exerted on the snowflake incorporated in the matrix prior to the decomposition mitigating information loss at lower sampling rates. We establish a linear relationship between snowflake shape porosity and minimum and maximum Dynamic Mode Decomposition eigenfrequencies, absolute decay or growth rates, and the wavenumber of the most energetic mode, linking particle geometry to wake flow characteristics. Higher porosity corresponds to more stable, small-scale flow structures and steady falling motion, while lower porosity promotes larger, unstable structures and falling trajectories with random particle orientations. These findings reveal the interdependence of snowflake geometry, wake flow dynamics, and falling behavior and highlight the importance of considering both spatial and temporal resolutions when dealing with modal analysis. This research contributes to improved predictions of snowflake falling behavior, with potential applications in meteorology and climate science.