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The barotropic instability of zonal flows due to infinitesimal normal-mode perturbations is considered, with the zonal flow assumed to be continuous and either monotonic or nonmonotonic and allowed to have one or more inflection points. A sufficient condition for instability is derived for this general flow profile that complements that of Arnol'd (1965), which restricted itself to the prediction of stability only.
The linear theory of deep zonal flows developed by Busse (1976) for the origins of deep motions of the atmospheres of Jupiter and Saturn is extended into the nonlinear regime. Relationships for the relative magnitudes of convective heat and momentum transports are formulated. A perturbation approach is taken to the problem, with the amplitude of the convection serving as the small parameter, and the basic equations being expanded in terms of the Prandtl number. The Boussinesq approximation is employed, together with an assumption of a low Rossby number for the Jovian and Saturn atmospheres. Differences in the amplitude of the Jovian equatorial jet relative to that of Saturn are explored in terms of a low equatorial convective heat flux on Jupiter.
Integrations of the linear stability problem, in the present numerical investigation of weakly nonparallel zonal flows barotropic instability having localized intense shear regions, reveal the existence of unstable localized wave packets. The spatial structure and eigenfrequencies of these packets depend on two parameters measuring the degree of supercriticality and the zonal length scale of the shear region. It is found that instability structure is defined by conditions ensuring the decay of the wave packet at infinity, and the transition from long to short waves across a turning point region that is controlled by nonparallel effects.
Gierasch et al. (1979) have shown that the question of the stability of zonal flows on Jupiter is influenced strongly by the lower boundary condition. In the case of Jupiter, the troposphere rests above a deep layer of fluid which is probably extremely close to adiabatic. The present study extends the earlier investigations to a wider range of conditions, taking into account the nongeostrophic limit and the presence of horizontal shear. The major difference between the behavior of the model derived in the study and the behavior of a model with a rigid lower boundary, corresponding to the terrestrial conditions, is that baroclinic instability by the Eady mechanism is suppressed. The influence of beta (Charney-type instability) operates only at the top of the troposphere, not at its base. The suppression of the Eady modes seems to apply all the way down to the nongeostrophic limit where the Rossby number is order unity.
In order to reexamine the magnitude differences of the Jovian atmosphere's jets, as determined by Voyager 1 and 2 images, a novel approach is used to ascertain the zonal mean east-west component of motion. This technique is based on digital pattern matching, and is applied on pairs of mapped images to yield a profile of the mean zonal component that reproduces the exact locations of the easterly and westerly jets between + and - 60 deg latitude. Results have been obtained for all of the Voyager 1 and 2 cylindrical mosaics; the correlation coefficient between Voyagers 1 and 2 in mean zonal flow between + and - 60 deg latitude, determined from violet filter mosaics, is 0.998.
In order to reexamine the magnitude differences of the Jovian atmosphere's jets, as determined by Voyager 1 and 2 images, a novel approach is used to ascertain the zonal mean east-west component of motion. This technique is based on digital pattern matching, and is applied on pairs of mapped images to yield a profile of the mean zonal component that reproduces the exact locations of the easterly and westerly jets between + and 60 deg latitude. Results were obtained for all of the Voyager 1 and 2 cylindrical mosaics; the correlation coefficient between Voyagers 1 and 2 in mean zonal flow between + and - 60 deg latitude, determined from violet filter mosaics, is 0.998.
Voyager imaging, infrared, and radio observations for Saturn have been recently interpreted by Smith et al. (1982) as an indication that the jet streams observed at the cloud tops extend to depths greater than the 10,000-bar level. This analysis assumes a maximum latitudinal temperature contrast of a few percent, a mean atmospheric rotation rate at depth given by Saturn's ratio period, and no variation with latitude of the bottom pressure level for the zonal flow system. These assumptions are not, however, firmly constrained by observation. The diagnostic analysis of plausible alternative configurations for Saturn's atmospheric structure demonstrates that a thin weather layer system (confined at mid to high latitudes to levels above 200 bar) cannot be excluded by any of the available observations. A quantitative estimate of the effects of moisture condensation (including the differentiation of mean molecular weight) suggests that these might provide the buoyancy contrasts necessary to support a thin-layer flow provided that Saturn's outer envelope is enriched approximately 10 times in water abundance relative to a solar composition atmosphere and strongly differentiated with latitude at the condensation level.
A simple model of the equatorial zonal jet in the giant planets is studied in which the flow is assumed uniform on cylinders concentric with the spin axis, and viscous and magnetic torques on each cylinder are balanced. This 'Taylor constraint' is solved simultaneously with the dynamo equation to obtain the velocity and magnetic field in the equatorial plane. The model is used to reproduce the widely differing jet widths of Jupiter and Saturn eddy viscosity of 2500 sq cm/s. For Saturn, the model has a large magnetic Reynolds number where the Chandrasekhar number Q = 1, and hence exhibits substantial axisymmetrization of the field in the equatorial plane.
The response of linear planetary wave 2 to changes in the isentropic zonally symmetric distribution of potential vorticity (PV) is investigated numerically. Wave 2 is sensitive to the width and position of a region where the meridional derivative of PV is weak, denoted the 'surf zone', in the middle stratosphere. A narrow surf zone leads to an amplification of wave 2, and confines some of its Eliassen-Palm wave activity in high latitudes. For wider surf zones the wave activity is concentrated near the associated critical surface, and the amplitude of the wave decreases. Large changes in the wave amplitude and in the distribution of its activity are associated with the subtle changes in the zonal winds produced by modest modifications in the distribution of PV. Basic states that include regions of reversed meridional gradients of PV lead to wave overreflection and strong poleward focusing of wave activity. The amplitude of wave 2 is enhanced in the presence of negative gradients, with large responses occurring for eastward traveling waves.
A closed-loop, overlapped, velocity-coupling procedure has been utilized to combine a two-dimensional potential flow panel code and a Navier-Stokes code. The fully coupled, two-zone code has been used to compute the flow past a NACA 0012 airfoil. For this case, the zonal method has shown that the grid domain size can be reduced to 0.14 chord lengths with less than 1 percent loss in accuracy. Further, the required computation time is reduced by a factor of approximately four.
A linearized barotropic model on a sphere is used to study the stability of a basic state composed of a westward-moving wave and a zonal mean jet. It is found that the inclusion of a very weak jet in the basic state dramatically alters the stability of the flow. The alteration of stability characteristics for realistic summer and winter jets is discussed.
A linear, primitive equation stationary wave model having high vertical and meridional resolution is used to examine the sensitivity of orographically forced (primarily by Himalayas) stationary waves at middle and high latitudes to variations in the basic state zonal wind distribution. We find relatively little sensitivity to the winds in high latitudes, but remarkable sensitivity to small variations in the subtropical jet. Fluctuations well within the range of observed variability in the jet can lead to large variations in the stationary waves of the high latitude stratosphere, and to large changes even in tropospheric stationary waves. Implications for both sudden warmings and large-scale weather are discussed.
Voyagers 1 and 2 narrow angle frames are used to obtain displacements of features at resolutions of 130 km over time intervals of 1 Jovian rotation. It is shown that the mean zonal velocity profile does not change by a measurable amount between Voyagers 1 and 2, which is consistent with previous observations. It is also shown that the curvature of the velocity profile vanes varies with latitudes in the range from -3 beta to +2 beta. The barotropic stability criterion is violated at 10 latitudes between + and - 60 deg, and the rate of conversion of eddy kinetic energy into zonal mean kinetic energy is in the range from 1.5 to 3.0 per sq Wm for a layer 2.5 bar deep. The rate of energy conversion is more than 10% of the total infrared heat flux for Jupiter, as compared to the earth where it is only 0.1% of the infrared, which suggests that the two planets possess fundamentally different thermomechanical energy cycles.
Observations show that the westerly acceleration of the equatorial quasi-biennial oscillation (QBO) can be accounted for by Kelvin waves, but that there is a deficiency in the easterly acceleration due to Rossby-gravity waves. Rossby waves and westward propagating gravity waves have been suggested as alternative sources for the easterly acceleration. The possible role of these two wave modes has been tested in a two-dimensional model of the QBO. When the easterly acceleration is due to Rossby waves, the zonal-mean response is steady; when it is due to gravity waves, an oscillation with some features similar to the QBO occurs, but it is of short period and weak amplitude. A similar result occurs when a standing-wave forcing pattern is imposed. These results suggest that Rossby waves play only a minor role in the QBO, and that while the Rossby-gravity mode is essential, other gravity modes may also be important for the easterly phase.
The forms and behavior of baroclinic instabilities occurring in a particularly simple model Jovian atmosphere are studied. First, an extension of the quasi-geostrophic model developed for the earth's atmosphere is used. The second model assumes that the lower-layer perturbation is allowed to be nonhydrostatic, since on Jupiter the disturbance depth scale in the lower layer may be comparable to or greater than the horizontal scale. The results obtained show the importance for the upper-layer meteorology of the interface boundary condition with the lower fluid, which is radically different from the rigid lower boundary of the earth's troposphere.
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We have derived a simple analytic solution showing how the Sun's global oscillations (g-modes) can drive east-west flows at low latitude deep inside the Sun. This flow is analogous to the Quasi Biennial Oscillation in the Earth s upper atmosphere. It has an observed period of 1.3 years in the solar case but its cause was not known until we published an explanation in a Letter to the Editor a few months ago. Now we give full details of the model and show how it can be used to limit the range of g-modes that can be actively driving the reversing flows. A nonlinear feedback feature of the model is that the flow itself creates the turbulent dissipation that extracts momentum from the g-modes that, in turn, drives the flow.
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