An Equatorial Thermal Wind Equation: Applications to Jupiter

A fundamental tool of GFD is the Thermal Wind Equation (TWE), which relates the vertical shear of the horizontal wind to the horizontal temperature gradient. Unfortunately, the TWE is invalid at and near the equator because the Coriolis force goes to zero and the Rossby number becomes large. Moreover, at some latitudes, even if the Rossby number is small, the TWE is ill-conditioned because it requires division by a small number. We have derived a well-conditioned ``Equatorial Thermal Wind Equation'' (EQTWE) that relates the vertical derivative of the east-west velocity to the second-derivative of the temperature in the north-south direction that is valid at the equator and up to latitudes of 18^o and whose validity is independent of the traditional Rossby number. We apply the EQTWE to the Jovian wind measured by the Galileo probe Doppler wind experiment to reveal thermal anomalies at the Jovian equator at altitudes below 1~bar and show that they imply 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. At altitudes above 1 bar we use IR temperatures and the EQTWE to determine velocities and show that there is a fast 205 m/s stratospheric jet at 3 mbar.