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Home/Biophysics, Fluids & Geoscience/Ekman Spiral in the Ocean

Ekman Spiral in the Ocean

Wind stress, Coriolis f, eddy viscosity A_z: classical Ekman spiral of horizontal velocity with depth; deflection angle.

Ocean parameters

45 °
0.05 m²/s
0.12 m/s

Steady Ekman solution u + iv = V₀ exp((−1 + isgn(f)) z/δ) with δ = √(2A_z/|f|): horizontal velocity rotates and decays with depth. Wind-driven surface stress sets V₀ here as a slider; the hodograph (u,v) traces a logarithmic spiral.

Measured values

Ekman depth δ31.1 m
Surface turn vs x̂3.8 °

f = 2Ω sin(lat): sign controls spiral handedness; near the equator δ diverges — stay away from |lat| < 5° in this model.

Live graphs

About this model

Steady wind stress on the ocean surface, Coriolis force, and vertical eddy viscosity A_z lead to the Ekman spiral: horizontal currents rotate and decay with depth on a scale δ = √(2A_z/|f|). Hodographs of (u, v) trace a logarithmic spiral; surface deflection relative to wind illustrates Ekman transport direction.

Who it's for: Physical oceanography or atmosphere boundary-layer introductions.

Key terms

  • Ekman spiral
  • Coriolis parameter
  • Eddy viscosity
  • Boundary layer

How it works

Wind stress, Coriolis parameter, and vertical eddy viscosity set the Ekman depth and the turning of horizontal currents with depth — the classic spiral behind upwelling and ice-drift deflection.

Frequently asked questions

What happens near the equator?
f → 0 makes δ diverge; the model is not valid there—use mid-latitude settings.