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

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.

In the open-basin Sverdrup balance approximation,The maximum is at $y=0$. Evaluating the exact finite-friction solution instead gives its largest northward velocity at the eastern side of the equator, about $4.96\mathrm{m}{\mathrm{s}}^{-1}$. Thus the requested scale is roughly $5\mathrm{m}{\mathrm{s}}^{-1}$ northward; the exact model also resolves variation across the open basin.

To return the broad interior transport, the western boundary current has opposite sign and characteristic peakThe leading exponential profile retains the smaller interior offset, $v(0)\simeq (F_0/\beta )(1-L/{\delta }_W)\simeq -52.1\mathrm{m}{\mathrm{s}}^{-1}$. Because $\gamma L\simeq 0.593$ is not very small, the exact two-wall solution gives a more accurate linear-model peak:All three evaluations identify an intense southward western boundary current, with peak at $x=0,y=0$, of order tens of metres per second. They are predictions of the stated steady linear barotropic model. Nonlinear advection, stratification and the actual basin geometry could alter them substantially; the calculation does not establish that real Pluto winds attain these values.