Planetary Convection Research Articles

Convection driven zonal flows and vortices in the major planets.

The dynamical properties of convection in rotating cylindrical annuli and spherical shells are reviewed. Simple theoretical models and experimental simulations of planetary convection through the use of the centrifugal force in the laboratory are emphasized. The model of columnar convection in a cylindrical annulus not only serves as a guide to the dynamical properties of convection in rotating sphere; it also is of interest as a basic physical system that exhibits several dynamical properties in their most simple form. The generation of zonal mean flows is discussed in some detail and examples of recent numerical computations are presented. The exploration of the parameter space for the annulus model is not yet complete and the theoretical exploration of convection in rotating spheres is still in the beginning phase. Quantitative comparisons with the observations of the dynamics of planetary atmospheres will have to await the consideration in the models of the effects of magnetic fields and the deviations from the Boussinesq approximation.

Convection in a rotating cylindrical annulus Part 3. Vacillating and spatially modulated flows

The problem of convection driven by radial buoyancy in a rotating cylindrical annulus with conical end surfaces represents one of the basic models of rotating fluid dynamics with applications to convection in planets and stars. Although only two-dimensional equations govern the flow in the limit of high rotation rates, a surprising variety of different states of motion can be found. In this paper earlier numerical work is extended by the consideration of rigid boundary conditions at the cylindrical walls and by a study of spatially modulated convection

High Rayleigh number convection with strongly variable viscosity: A comparison between mean field and two‐dimensional solutions

We have studied single‐mode mean field equations associated with variable viscosity convection for both steady state and time‐dependent situations. Steady state mean field solutions can be obtained by treating the governing mean field equations as two coupled fourth‐order differential systems, which are solved as a series of coupled two‐point boundary value problems with underrelaxation. Steady solutions can be achieved in which there can exist viscosity contrasts exceeding 108 and interior Rayleigh numbers of 0(109). For comparison with two‐dimensional solutions we have employed results derived from two finite element methods. Both temperature‐dependent and temperature‐ and pressure‐dependent viscosity with the surface viscosity fixed have been studied. Our results show that the differences between the two approaches grow with both viscosity contrast and convective vigor. The steady state Nusselt numbers and interior temperatures are greater in the case of mean field solutions. The power law index β governing the relationship between the interior Rayleigh number and the Nusselt number is larger for the mean field. Comparison of time‐dependent solutions shows that one can monitor rather faithfully the evolution of the averaged interior temperature and surface heat flow over a long time scale with the mean field method. Initially, thermal instabilities originating from the mean field boundary layers are found to be correlated with two‐dimensional boundary layer instabilities and are much more violent in character and cause large oscillations of the surface heat flow. The time scales associated with the secular variations of the Urey number, representing the ratio of the heat production and the surface heat loss, agree well between the two approaches. These results suggest that the mean field equations may serve as an efficient vehicle for studying planetary convection with complicated physics.

The evolution of the moon: A finite element approach

Thermal convection has considerable influence on the thermal evolution of terrestrial planets. Previous numerical models of planetary convection have solved the system of partial differential equations by finite difference methods, or have approximated it by parametrized methods. We have evaluated the applicability of a finite element solution of these equations. Our model analyses the thermal history of a self-gravitating spherical planetary body; it includes the effects of viscous dissipation, internal melting, adiabatic gradient, core formation, variable viscosity, decay of radioactive nucleides, and a depth dependent initial temperature profile. Reflecting current interest, physical parameters corresponding to the Moon were selected for the model. Although no initial basalt ocean is assumed for the Moon, partial melting is observed very early in its history; this is presumably related to the formation of the basalt maria. The convection pattern appears to be dominated by an L-2 mode. The present-day lithospheric thickness in the model is 600 km, with core-mantle temperatures close to 1600 K. Surface heat flux is 25.3 mW m−2, higher than the steady state-value by about 16%. The finite element method is clearly applicable to the problem of planetary evolution, but much faster solution algorithms will be necessary if a sufficient number of models are to be examined by this method.

A model of the atmospheric convection zone with a large increase of rotation velocity between its bottom and top

A simple model of a slowly rotating stellar or planetary atmospheric convection zone is considered supposing that only growing convective perturbations contribute to the value of nonlinear azimuthal force maintaining the differential rotation of the zone. Besides, the angular velocity of rotation is assumed to be dependent only on the distance to the center. It turns out that in this model some resonance phenomenon is possible, due to which a structure can be formed with a large rotation velocity gradient. This is caused by the interaction of two different azimuthal forces, one being proportional to either the angular velocity or its derivatives, while the other being determined by some mean value of the same velocity. The latter force appears in consequence of different time-dependence of the perturbations in rotating versus nonrotating convective zones. A hypothesis is put forward that fast rotation of the upper atmosphere of Venus is due to such resonance interaction.

Theory of the Earth-synchronous rotation of Venus

CARPENTER1 noted in 1966 that the radar observations of the rotation period of Venus gave a figure remarkably close to one at which Venus would present the same aspect to the Earth at each inferior conjunction. Goldreich and Peale2 discussed this as a possible resonance with a gravitational couple exerted by the Earth on a permanent transverse quadrupole moment of Venus, but noted that such a couple would be expected to be much smaller than that due to the Sun acting on the solid body tide. The rotation would continue to slow down due to tidal friction, and could not have been arrested in the resonance. We therefore proposed3 that the solar couple on thermal atmospheric tides might be expected to apply an acceleration to the spin of Venus, thus opposing the body tidal frictional deceleration. (An effect in that sense occurs for the Earth.) The two opposed torques would have a different dependence on the rotation speed of Venus, and might balance at a particular value. As the rotation speed approached this value, the torque necessary for capture into a resonance would have become very small, and the effect exerted by the Earth might then be sufficient. A diurnal pressure wave of as little as 1 mbar could balance the body tide. Ingersoll and Dobrovolskis4 have reconsidered this suggestion, and attempted a quantitative calculation of the atmospheric tide. Although their result seems to favour the theory, we show here that their approach is not valid. Ingersoll and Dobrovolskis consider a quasi-static atmosphere heated diurnally, and then calculate the mass distribution and hence the solar couple that results. But the quasi-static assumption is not justified for the known circumstances on Venus. Wind speeds must be expected5, and have indeed been observed6, that cause an advection of heat substantially faster than the motion of the subsolar point over the surface (∼4 m s−1); in these circumstances the atmospheric mass distribution will be determined by the dynamics of the convecting atmosphere. (The acceleration terms rather than temperature make the main contribution to horizontal variations of pressure and density.) A secure result cannot be obtained until the flow patterns and velocities are known, from a detailed theory of planetary convection, or from direct observation.

Plate tectonics and planetary convection

A series of azimuthal–equidistant map projections, centered on each of the plates of lithosphere, is used to demonstrate the high degree of ordering and symmetry in the major plates. The Pacific and African plates are approximately circular with a radius of 60°. The entire pattern is dominated by these two major plates, exactly antipodal to one another in the form of a dipole. Between the two 'circular' plates is a ring of elliptical plates with irregular boundaries but a organized geometric interrelationship. The average major and minor axes of the 'elliptical' plates, measured at the center of the earth, are 62° ± 6 °and 30° ± 5°, and the major axes are oriented at angles of 56° ± 3 °to lines joining the center of the African plate. The centers of the 'elliptical' plates are arranged within 6° ± 3 °of a great circle path through the North pole. This organized distribution of the major plates is most likely the result of convection currents involving the entire mantle, from the lithosphere to the core. To a first approximation, the convective pattern may be modelled by a superposition of third order spherical harmonics, P03, P13, and P23 in a pattern that regressed from a first spherical harmonic, −P01.

Comments on planetary convection as applied to the earth

Comments on planetary convection as applied to the earth