Past exam of the physics of atmospheres and oceans course of the University of Oxford / 2021 / 6 / d / Solution

Use the positive rotation-rate convention implicit in the northward planetary vorticity gradient. One Pluto day is $T_P=6.4\times 86400=552960\mathrm{s}$. At the equator,The width of the western boundary current is thereforeHere $b=a_p\pi /3\simeq 1244\mathrm{km}$ is the full meridional scale, and $L=a_p(50\pi /180)\simeq 1037\mathrm{km}$. For these data the exact exponents give ${\lambda }^{-1}\simeq 89.7\mathrm{km}$, $\lambda L\simeq 11.56$ and $\gamma L\simeq 0.593$. The western layer is narrow, but $\gamma L\ll 1$ is only marginal. The leading estimates below should therefore be distinguished from evaluation of the exact linear model.