Snow Density Simulation: Globe Effect — 2D Stokes Settling and Flow Cell

Stokes settling

A small sphere in a viscous liquid obeys m dv/dt = (ρp - ρf) V g - 6πμ r v. The solution relaxes exponentially, v(t) = vs(1 - e-t/τ), with terminal speed vs = 2 (ρp - ρf) g r² / (9 μ) and response time τ = 2 ρp r² / (9 μ). Because τ is milliseconds, flakes follow the stirring flow closely while it lasts, then drift down at v_s.

What this view adds

A cross-section of the globe with the decaying stirring flow, 260 flakes integrated with the exact exponential relaxation step, and a graph of mean flake height against the Stokes prediction once the flow has died away.

Simplifications

Stokes drag needs Reynolds number below about 1; the readout warns when it is exceeded. The stirring is a decaying divergence-free cell pattern with a fixed 1.6 s decay, not a Navier-Stokes solution; flakes are spheres, do not interact, ignore added mass and wall drag, and slide along the glass. Liquid properties are rounded room-temperature values.