Ekman Spiral: Wind-Driven Ocean Currents

Forcing

Wind speed (10 m) 10 m/s

Latitude 45°

Turbulent eddy viscosity A_z 0.012 m²/s

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Ekman depth D

— m

Coriolis f

—

Surface speed

— cm/s

Surface deflection

—°

Net (depth-integrated) transport direction

—

How it works

A steady wind drags on the sea surface with stress τ = ρ_airC_dU², but the water doesn't simply flow downwind: Earth's rotation (Coriolis force) deflects it. Balancing wind stress, Coriolis force and vertical turbulent friction (eddy viscosity A_z) gives the Ekman spiral:

f  = 2Ω sin(latitude)              Coriolis parameter
D  = √(2·A_z / |f|)                Ekman depth scale
V0 = τ / √(ρ_water · A_z · |f|)    surface current speed

u(h) = V0 e^(−h/D) cos(45° − h/D)   (Northern Hemisphere)
v(h) = V0 e^(−h/D) sin(45° − h/D)
h = depth below surface (m)

Surface current sits 45° to the right of the wind in the Northern Hemisphere (left in the Southern) — never straight downwind.
Going deeper, the current keeps rotating the same way while its speed decays exponentially — tracing the spiral you see in the water column.
Net transport, integrated over the whole spiral, points almost exactly 90° to the right of the wind (left in the Southern Hemisphere) — this is the real mechanism behind coastal upwelling and downwelling.
Higher latitude → larger f → shallower, tighter spiral. More turbulent mixing (A_z) → deeper, broader spiral.

This is the classical model published by V. Walfrid Ekman in 1905 to explain why Arctic ice drifts 20–40° to the right of the wind, and it still underlies operational ocean forecasting today.

Wind direction Current, surface → deep Net transport (90° to wind)

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