Concept

Geophysical — where it appears

Belonging to the flows of a planet's oceans and atmosphere, where rotation and stratification dominate and the horizontal scales are thousands of times the vertical. Such flows are nearly two-dimensional, and what makes them so is the rotation rather than the geometry.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

$How long a fluid takes to forget it was not rotating. The fraction of solid-body rotation a container's interior has reached, against time, by the two available routes. The Ekman layers on the end walls pump fluid radially and carry angular momentum inwards in a hundred seconds; diffusion alone would need ten thousand.$

How long a fluid takes to forget it was not rotating

Spin a container of water and the fluid inside reaches solid-body rotation in a hundred seconds rather than the three hours diffusion would need. The shortcut is the thin layers on the end walls, and the advantage they give is exactly the reciprocal of the square root of the Ekman number.

viscous · Rotating

The barrier is pinched to nothing in one direction. Where the inverse cascade is stopped, drawn in the plane of wavenumbers. The curve is the scale at which a Rossby wave oscillates as fast as an eddy turns over, and inside it the cascade cannot proceed. It is not a circle: it closes to a point on the axis of modes with no variation in longitude, so the cascade runs on unimpeded towards the largest scales in exactly one direction — and what it makes there is a band.

A cascade that arrives as stripes

Two-dimensional turbulence sends its energy upward in scale and, on a plane, piles it into a pair of vortices filling the box. On a rotating planet one extra term in the vorticity equation blocks that in every direction but one, and what arrives at the large scales is not a vortex at all but a set of bands.

turbulence · Two-dimensional

Named alongside it

The objects these essays reach for when they reach for this one.

Angular momentum Anisotropy Boundary layer Diffusion Dimensionless Dispersion relation Ekman layer Inverse cascade Memory kernel Model limit Model validity Regime

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