= Prandtl ratio of scales
{c}
{title2=$H/L\sim f_0/N$}
The Prandtl ratio compares horizontal and vertical scales in rotating <density stratification>. In the <three-dimensional quasi-geostrophic potential vorticity> operator, horizontal curvature scales as $\psi/L^2$ and vertical stretching as $(f_0^2/N^2)\psi/H^2$. Comparable terms therefore require $H/L\sim |f_0|/N$. For constant $N$, the stretched coordinate $Z=(N/|f_0|)z$ makes the operator isotropic. This aspect ratio concerns rotational and stratification effects, not the viscous-to-thermal diffusivity <Prandtl number>.
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