Glacier Ice Flow Simulator (2D)

Ice Column

Ice thickness 150 m

Valley slope 8.0°

Ice temperature -5 °C

Cold, stiff ice — slow viscous creep.

Live Readout

Surface velocity

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Basal shear stress

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Rate factor A

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Depth-avg. velocity

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How it works

Glacier ice is not rigid — under its own weight it deforms slowly like a very viscous fluid, a process called internal creep. The relationship between stress and strain rate follows Glen's flow law: strain rate ε̇ = A·τⁿ, where τ is shear stress, n ≈ 3 (the standard exponent for polycrystalline ice), and A is a temperature-dependent rate factor — warmer ice is far softer and flows much faster.

For a slab of ice of thickness H resting on a slope of angle α, the shear stress grows linearly with depth: τ(z) = ρg(H−z)sin α, where z is height above the bed. Integrating the strain rate from the bed up gives the horizontal velocity profile: u(z) = u_b + (2A/(n+1))·(ρg sin α)ⁿ·[Hⁿ⁺¹ − (H−z)ⁿ⁺¹]. Shear is concentrated near the bed where stress is highest, so velocity increases slowly at first and then rises quickly toward the surface — the classic "S"-shaped profile seen when stakes drilled into a real glacier bend downhill over a season.

ρ = 900 kg/m³ (glacier ice density), g = 9.81 m/s²
A ranges from ~1.2×10⁻²⁵ Pa⁻³s⁻¹ at −20 °C to ~2.4×10⁻²⁴ Pa⁻³s⁻¹ at 0 °C (Cuffey & Paterson)
This model assumes cold-based ice (no basal sliding, u_b = 0) — pure internal deformation