Iceberg Ocean Drift (2D): Wind, Current and Coriolis Force on a Floating Ice Island

Presets

Live readouts

Graphs

Drift speed through time

Drift track (km east, km north)

Iceberg thickness and size relative to the start

Numerical checks

running...

How to use

Choose a preset and watch the berg drift while the track grows. Try: (1) Wind only, no Coriolis: the berg moves exactly downwind between the air and water speeds; (2) Labrador Current: the berg is turned to the right of the wind by the Coriolis force; (3) Calm: inertial loops, press Kick and compare the loop period with 2π/f in the readouts; (4) Warm water melt: H and L shrink on the size graph; (5) change the water density and read how the draft and freeboard change; (6) in 3D use the Under view to see the ice below the surface and lower the water transparency to hide it. Space pauses, R restarts.

The science

Floating. By Archimedes' principle a free-floating iceberg displaces its own weight of water, so the submerged fraction is

d / H = ρ_ice / ρ_water ≈ 917 / 1025 = 0.895

About nine tenths of the ice is below the surface; in fresh water (1000 kg/m³) it is even 92 %. Freeboard is only H - d, but it is the wind that acts on it, while the much larger draft d feels the ocean current.

Forces. For a square tabular berg of side L and thickness H (mass m = ρ_ice L² H, added mass factor 1.5 on the drag terms) the horizontal equation of motion in the Smith (1993) form is

m_eff dv/dt = ½ρ_a C_a A_a |V_a - v| (V_a - v) + ½ρ_w C_w A_w |V_w - v| (V_w - v) - m f k × (v - V_w)

with air drag area A_a = L (H - d), water drag area A_w = L d, C_a = 1.3, C_w = 0.9 and the Coriolis parameter f = 2Ω sin(latitude). The last term is the Coriolis force plus the sea-surface-slope (geostrophic pressure-gradient) force, written so that a berg at rest relative to the current feels no net force from them. Because the wind drag is large and the water drag is quadratic, the berg ends up drifting at a fraction of a metre per second and, in the northern hemisphere, to the right of the wind-plus-current direction; in the southern hemisphere to the left.

Inertial loops. With no drag at all, v rotates at angular rate f at constant speed: the inertial period is 2π/|f| (12.7 h at 70 degrees, 12 h at 30 degrees). Kick the berg in the calm preset and watch it loop; with drag the loops spiral into the steady drift.

Melting. Two simple parametrisations are used: basal melt M_b = 0.58 |V_w - v|^0.8 (T_w - T_i) / L^0.2 (m per day, relative speed in m/s, temperatures in degrees C, T_i = -4 degrees C) thins the berg, and wave erosion at the waterline M_e = S_s (T_a + 2)/12 (m per day, S_s the sea state 0 to 5) shrinks its side length by 2 M_e per day. Freeboard and draft follow from Archimedes at every moment.

Checks (run in the page). (1) the submerged volume fraction against ρ_ice/ρ_water; (2) with f = 0 and wind and current in line, the RK4 terminal speed against the closed form v = (V_a√K_a + V_w√K_w)/(√K_a + √K_w) where K = ½ρ C A; (3) the half period of the free inertial oscillation against π/f and conservation of speed; (4) the basal melt rate against a hand calculation.

Simplifications. A square berg with constant drag coefficients, no rotation of the berg, no sea ice, no wave radiation force, uniform wind and current in space and time, the geostrophic current equal to the specified current, and no calving or capsizing (see the separate calving and metacentric stability lab). The melt laws are empirical; real melt rates depend strongly on the local water column. The 3D scene runs a time-lapse, so the sea waves are only for appearance and do not move with model time.