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 Incoming links: Rossby number

Vertical-advection consistency criterion for log-pressure quasi-geostrophy 2026-10-05

For scales

U, L, D

, thermal balance estimates

w \sim f_{0} U^{2} / (N^{2} D)

. Density-weighted continuity gives horizontal ageostrophic flow of order

L w / min (D, H)

. It is small relative to

U

only if

ϵ_{a} = \frac{f _{0}^{2} L ^{2}}{N ^{2} D m i n ( D , H )} \frac{U}{∣ f _{0} ∣ L} ≪ 1.

This condition supplements small Rossby number and small relative variation

β L /∣ f_{0} ∣

of the Coriolis parameter.

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