Ekmara: Ekman Spiral
Mechanics, Chaos & Fluids arc, page 108 of 193. Back to The Pixelated Physics Universe
Who they are
Ekmara's hair coils down into the sea in a spiral of arrows, each one turned a little further right and a little weaker.
Ekmara is a character of the Mechanics, Chaos & Fluids arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
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.
$$ \begin{gathered} u + iv = V_0\,e^{i\pi/4}\,e^{(1+i)z/D}, \qquad z \le 0 \\ D = \sqrt{\frac{2\nu}{|f|}}, \qquad f = 2\Omega\sin\varphi \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $u,\ v$ | horizontal current components (east, north) | m/s |
| $i$ | imaginary unit | 1 |
| $V_0$ | surface current speed | m/s |
| $z$ | height, negative below the surface | m |
| $D$ | Ekman decay depth | m |
| $\nu$ | eddy viscosity | m²/s |
| $f$ | Coriolis parameter | 1/s |
| $\Omega$ | Earth's rotation rate, 7.292 × 10⁻⁵ rad/s | rad/s |
| $\varphi$ | latitude | rad |
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.
Sources
- Ekman (1905) On the influence of the earth's rotation on ocean-currents, Ark. Mat. Astron. Fys. 2(11), 1–52
- NOAA Ocean Service, Ekman transport
Crossovers
Ekmara meets Stratalat (Layered Latte Convection). Stratalat's layers come from two things diffusing at different rates. Ekmara's spiral comes from the Coriolis effect turning wind-driven flow with depth. Both are layered flows where a second effect makes a pattern.
Ekmara meets Seisma (Gutenberg–Richter Law). Ekmara's spiral moves the ocean's surface waters. Seisma's quakes move the crust. Both are Earth sciences that use physics to read a planet in motion.
Wear the lore
Concept keywords: Ekman Spiral, Ekmara, Mechanics, Chaos & Fluids, physics lore, Pixelated Physics