Ekmara

Ekmara's hair coils down into the sea in a spiral of arrows, each one turned a little further right and a little weaker.

The Physics

Nansen noticed during the Fram expedition that drifting sea ice moved to the right of the wind. V. W. Ekman explained it in 1905. Wind drags the surface layer, the Coriolis effect turns each layer to the right in the Northern Hemisphere, and friction passes the drag downward, so the current turns and weakens with depth in a spiral.

In the idealised model the surface current runs 45° to the right of the wind and the net, depth-integrated transport is 90° to the right.

u + iv = V₀ e^(iπ/4) e^((1+i)z/D), D = √(2ν/|f|), f = 2Ω sin φ

• u, v: current components (m/s), wind along +y
• V₀: surface current speed (m/s)
• z: depth coordinate, z ≤ 0 (m)
• D: decay depth (m)
• ν: eddy viscosity (m²/s)
• f: Coriolis parameter (1/s)
• Ω: Earth's rotation rate (rad/s)
• φ: latitude

V. W. Ekman, Arkiv för matematik, astronomi och fysik 2, no. 11 (1905).

Honest caveat: The 45° and 90° hold for a steady, deep ocean with constant viscosity and no boundaries. Real oceans show a smaller turning angle because viscosity is not constant. In the Southern Hemisphere the turning is to the left.

On the shirt

Front: Ekmara, the pixel-art character, with “THE EKMAN SPIRAL”. Back: the 45° and 90° rules, the spiral solution, the decay depth, the ideal-model note and Ekman's 1905 paper. Printed on a unisex tee.