## Dynamical processes

5.1 INTRODUCTION

In Chapter 4 we discussed the vertical profiles of temperature, pressure, composition, and clouds of the giant planet atmospheres, and also briefly discussed transport mechanisms such as convection and eddy mixing. Of course the real atmospheres of planets are three-dimensional and thus to understand fully the observations of ground-based telescopes and spacecraft missions, we need to understand how planetary atmospheres move and how heat and material are transported, not just vertically, but horizontally as well. In this chapter we will consider the basic equations of fluid motion in rotating planetary atmospheres and see how these theoretical considerations relate to the observed winds, clouds, and storm systems observed in the atmospheres of the giant planets.

5.2 MEAN CIRCULATION OF THE GIANT PLANET ATMOSPHERES

In the upper layers of planetary atmospheres, where the atmosphere starts to become optically thin, the heating of the atmosphere, both through absorption of sunlight and by absorption of internal energy, provides a source of kinetic energy for atmospheric motion through a number of cycles akin to that of a heat engine shown in Figure 5.1. Consider local heating of the atmosphere. Air near the bottom of the atmosphere is heated quasi-isothermally which (in regions where free convection or forced convection occur) causes the air to rise and cool adiabatically. The air then radiates energy to space in the IR at the top of the atmosphere (where it is optically thin) causing it to cool further before it descends again and heats adiabatically until it reaches the bottom of the atmosphere and the cycle repeats. The integrated area of thep/V cycle is the work done per cycle, or equivalently is proportional to the rate at which thermal energy is converted into kinetic energy on a local scale. On a larger scale, solar heating is strongest at subsolar latitudes and least near the poles (except for Uranus, which spins on its side and where the subsolar latitude varies between the equator and poles during the course of a Uranian year). Hence, in the absence of atmospheric motion, the tropics would become warmer than the poles. Such differential heating creates pressure gradients, and atmospheres in general respond to this by moving in such a way as to minimize the temperature differences over the planet and become barotropic. Atmospheric motions are found to efficiently counterbalance differential solar heating on all of the giant planets. Even Uranus, which for large fractions of its orbit receives sunlight at either the North or South Pole only, has negligible equator-to-pole temperature difference at levels where p > 0.5 bar. In

Figure 5.1. Conversion of thermal energy into energy by a Carnot heat engine moving along path abcd. The dotted lines are isotherms and dash-dotted lines are adiabats. The area of the enclosed loop is proportional to the rate at which thermal energy is converted into work.

addition to this differential solar heating, all of the giant planets, with the exception of Uranus, have large internal heat sources resulting from Kelvin-Helmholtz contractions and internal differentiation. It would appear that the circulations of the atmospheres are arranged such that more of this internal energy is released away from the subsolar latitudes since the net thermal emission to space is found to be almost independent of latitude (as was discussed in Chapter 1).

Before we can go on to describe the general circulations of the giant planets further we need to outline some basic atmospheric dynamics.