Main

This feature cannot be reproduced in conventional shallow-atmosphere models. A set of idealized simulations of single fluid-layer flows on a rotating sphere, starting from a random initial condition4, explains both the magnitude and the number of jets well, but has an important defect in that it produces retrograde (easterly) jets at the equator. The reason for this defect is that turbulent horizontal mixing of the planetary rotational vorticity, which has opposite signs in the two hemispheres, gives rise to a slower (retrograde) atmospheric rotation than the planetary value over the equator. The sign of the parameter β, defined as the rate of change of the Coriolis parameter with latitude, dictates the sign of the jets (see equation (2.4) in ref. 5) by the conservation of potential vorticity6, which measures the total strength of the atmospheric vorticity tube, in the course of this mixing process7.

The atmospheres of Jupiter and Saturn are much deeper than Earth's atmosphere, however, making possible completely different dynamics8,9,10 in which the flows are deep, extending from one hemisphere to another. These flows are homogeneous in the direction of the axis of planetary rotation when the planetary interior is well mixed by thermal convection8. A single fluid layer, confined within the planetary sphere, therefore describes these deep flows10.

Analogous dynamics that conserve a potential vorticity govern this system, which is defined in terms of the deep fluid tubes parallel to the axis of planetary rotation. The resulting β, which now measures the rate of change in the length of fluid tubes with latitude, takes the opposite sign2,9. Consequently, the equatorial jet also has an opposite sign, as has been observed. Lateral transport of stronger potential vorticity, owing to longer fluid tubes, from higher latitudes to the equator, gives rise to faster (prograde) rotation.

To demonstrate this, we run the model, assuming constant density and no convective buoyancy forcing, for a long period, starting from a random state with wind variance of 100 m s−1 and 200 m s−1 for Jupiter and Saturn, respectively. These magnitudes are comparable to those observed1,4. In both cases, we obtain the prograde equatorial jets of the correct width and magnitude, and also with an indication of multiple jets (Fig. 1).

Figure 1: Simulated zonal winds (solid lines) and actual observations (dashed lines) for Jupiter and Saturn, after 300 and 100 planetary rotations, respectively, from an initial random state.
figure 1

Here, for numerical stability, spherical geometry is replaced by a cylindrical wall parallel to the axis of planetary rotation at 99% of the planetary radius, which intersects with the planetary surface at ±8.1° latitude. The plot assumes that homogeneous winds on this cylindrical wall are directly observed at the cloud tops of the lower latitudes. Full modelling details are available from the authors.

Another attractive feature of our 'deep' model is that the magnitude of β values is greater, which relaxes the wind-shear stability criterion9 and opens the way for obtaining steeper high-latitude jets, in accordance with observations. This is another feature that conventional shallow models can reproduce only with difficulty. Inclusion of a convective buoyancy force8 would give rise to steeper jets in our deep model.