Series

Geostrophy — the series

One essay so far on this idea, and more questions about it than one essay answers.

$The error in the balance is the number itself. The fractional error in the geostrophic wind, against the Rossby number, on logarithmic axes. It is a straight line of slope one through the origin, and that is not an approximation: keeping the centripetal term gives V_g/V = 1 ± Ro exactly, so the error and the number are the same quantity. The geostrophic wind is one per cent right at Ro = 0.01 and a hundred per cent wrong at Ro = 1, which is the value the number is named for and is quoted as the boundary of the approximation.$
The balance that is its own error

Geostrophic balance is licensed by the Rossby number being small, and the fractional error in the geostrophic wind is the Rossby number — exactly, not approximately. So the balance everybody uses at Ro of order one is a hundred per cent wrong, and the same quadratic has a hard limit at a quarter that no anticyclone can pass.
part 1 · regimes