Global climate by Rossby number in the Solar system planets

On the largest scales, planetary climates can be described by their Rossby number ($\mathit{\text{Ro}}$). $\mathit{\text{Ro}}$ is in response to $Gr\mathrm{/}R{e}^2$ , where Gr is the Grashof number and Re is the Reynolds number. We here simplify $Gr\mathrm{/}R{e}^2$ as h, where $h=H\mathrm{/}{H}_{Earth}$ with $H=gP\mathrm{/}(2\pi V_e)$ for a planet with surface gravity $\mathit{\text{g}}$, rotation period $\mathit{\text{P}}$ and equatorial velocity V\textsubscript{e}. Unlike $\mathit{\text{h}}$, $\mathit{\text{Ro}}$ is difficult to obtain because of a large diversity in observation. We perform on an in-depth literature search on average (av) and maximum (mx) wind velocity for each planet in the Solar system by various observational methods and by altitude. We explore a correlation between $\mathit{\text{Ro}}$ and $\mathit{\text{h}}$ expressed as a power law with index $\alpha$ based on wind velocities of planets in the Solar system. We obtain a correlation between $\mathit{\text{Ro}}$ and $\mathit{\text{h}}$ with $\alpha =0.56$ (av) and $\alpha =0.52$ (mx). Earth’s $H=H_{Earth}$ ($h=1$) is primarily due to lunar tidal interaction, given our relatively distant habitable zone (HZ) to the Sun. Our positive correlation, therefore, suggests exoplanet-moon systems as the `go-to-place’ in our searches for potentially advanced life in exosolar system.