Global climate by Rossby number in the Solar system planets

Abstract

On the largest scales, planetary climates can be described by their Rossby number (\textit{Ro}). \textit{Ro} is in response to $Gr/Re^2$ , where Gr is the Grashof number and Re is the Reynolds number. We here simplify $Gr/Re^2$ as h, where $h=H/H_{Earth}$ with $H=gP/(2\pi V_e)$ for a planet with surface gravity \textit{g}, rotation period \textit{P} and equatorial velocity V\textsubscript{e}. Unlike \textit{h}, \textit{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 \textit{Ro} and \textit{h} expressed as a power law with index $\alpha$ based on wind velocities of planets in the Solar system. We obtain a correlation between \textit{Ro} and \textit{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.