Vertical-advection consistency criterion for log-pressure quasi-geostrophy
= Vertical-advection consistency criterion for log-pressure quasi-geostrophy
For scales $U,L,D$, thermal balance estimates $w\sim f_0U^2/(N^2D)$. Density-weighted continuity gives horizontal <ageostrophic flow> of order $Lw/\min(D,H)$. It is small relative to $U$ only if
$$
\epsilon_a=\frac{f_0^2L^2}{N^2D\min(D,H)}\frac{U}{|f_0|L}\ll1.
$$
This condition supplements small <Rossby number> and small relative variation $\beta L/|f_0|$ of the <Coriolis parameter>.