Coastal Upwelling: Ekman Transport

Wind Forcing

Wind speed 10 m/s

Wind direction (blowing toward) 0°

Latitude 30° N

Vertical mixing (eddy viscosity) 0.020 m²/s

Coastal Response

— compute the flow —

Wind stress τ

0 Pa

Ekman depth D

0 m

Surface speed

0 cm/s

Net transport

0 m²/s

How it works

Wind blowing over the ocean drags the surface via a stress τ = ρ_airC_dU². The Coriolis force then deflects the resulting current — to the right of the wind in the Northern Hemisphere, to the left in the Southern Hemisphere — and friction (eddy viscosity A_v) hands that deflection down through the water column, so each depth turns a little further and the current weakens exponentially. That corkscrew of vectors is the Ekman spiral:

D = √(2A_v / |f|)         Ekman depth scale
f = 2Ω sin(latitude)      Coriolis parameter
u,v(z) = V₀ e^(z/D) · [rotated 45°+z/D
          from the wind direction]

What matters for the coast is not the surface current but the depth-integrated Ekman transport, which points exactly 90° to the right of the wind (NH) — regardless of wind direction relative to the spiral itself:

M = τ / (ρ_water · f),  oriented 90° right of wind (NH)

When that net transport points offshore, surface water is pushed away from the coast and cold, nutrient-rich deep water rises to replace it — upwelling. This is why the California, Peru/Humboldt and Benguela current systems, with equatorward alongshore wind, are among the most productive fisheries on Earth.
When it points onshore, surface water piles up against the coast and is forced downward — downwelling, which suppresses productivity.
Stronger wind (larger τ) and shallower mixing (smaller D) sharpen the spiral and speed up the response; near the equator |f|→0 and the whole balance breaks down (the slider is clamped a few degrees off the equator for that reason).

Ekman spiral (current vs. depth) Net (depth-integrated) transport Wind

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