An equatorial thermal wind equation: Applications to Jupiter

Abstract

To relate the vertical wind shear to horizontal temperature gradients at and near the equator, we derive an “Equatorial Thermal Wind Equation” (EQTWE) using a minimum set of assumptions that are easily satisfied for the atmospheres of all the giant planets and Earth. Similar to the textbook Thermal Wind Equation (TWE), the EQTWE requires a small Rossby number, but the relevant Rossby number for the EQTWE depends on the velocity and length scales of the equatorial flows, and on the Coriolis parameter at the north pole (which is large), rather than the Coriolis parameter at the equator (which goes to zero). Unlike the TWE, the EQTWE is valid only for the east-west component of the wind. We apply the EQTWE to the Jovian wind measured by the Galileo probe Doppler wind experiment at jovicentric latitude 6.53°N (7.46°N jovigraphic), which is valid because the EQTWE is accurate at latitudes θ < 18°. Assuming that this wind profile holds at all longitudes, the EQTWE shows that near the equator at altitudes at 0.8 bar < P < 5 bar, the atmosphere is anomalously cool with respect to the surrounding flow, and at 5 bar ≤ P < 13 bar, it is warm. These anomalies imply adiabatic up-welling (down-welling) at 0.8 bar < P < 5 bar (at 5 bar ≤ P ≤ 13 bar), which suggests a Jovian global circulation model with two layers of Hadley cells, with an upper layer like the one on Earth, and the lower has cells with the opposite rotation. Applying the EQTWE to CIRS temperatures at altitudes above 330 mbar, shows that the large vertical wind shears measured by the Galileo probe extend to higher altitudes, and at 3 mbar create a stratospheric equatorial jet with a velocity of 205 m/s (almost 50% faster than the speed that had been obtained earlier with the TWE).