Planetary Convection Research Articles

A Tectonic Manifesto

AbstractTectonics is the scientific discipline that studies the relationship between planetary convection and surface deformation and magmatism. In recent years global tectonic regimes and planetary evolution have become foci of astronomical and planetological research dealing in particular with potential habitability of planets orbiting other stars in our galaxy (exoplanets). This broadens the scientific impact of “tectonics” and makes it useful to outline a few guiding principles. For many, the term “tectonics” is synonymous with Plate Tectonics on Earth, but it should not be limited to only the planet we know best. Specifically, the concept should be generalized to encompass other rocky planets and moons in our Solar System and exoplanets. This article summarizes 15 general concepts about how such bodies are expected to behave.

An Argument in Favor of Magnetic Polarity Reversals Due to Heat Flux Variations in Fully Convective Stars and Planets

Low-mass M dwarf stars, T Tauri stars, as well as planets such as the Earth and Jupiter are permeated by large-scale magnetic fields generated by the convection-driven dynamo operating in their convection zones. These magnetic fields are often characterized by a significant time variability, most prominently expressed by the inversions of their polarity, denoted as reversals, whose mechanism has not been completely understood. This work aims to gain some insights into the mechanism that generates these reversals. With this purpose, a simplified nonlinear model is developed to investigate the role played in polarity reversals by the convective heat transfer occurring in stellar and planetary convection zones. A model result is the enhancement of the global heat transport before polarity reversals, showing the crucial role that heat transport might play in their occurrence. This role is elucidated by considering that a reversal has a greater than 70% probability of occurring during a burst of convective heat transport. This high probability has been found in 94 out of 101 numerical simulations obtained by changing characteristic model parameters. Moreover, the causal relationship between the convective heat flux growth and the magnetic field variations is highlighted by the temporal antecedence of the former relative to the latter and by convergent cross mapping, namely a statistical test for detecting causality. It would thus be expected that higher levels of temporal variability in the planetary and stellar magnetic fields may be correlated to a higher heat transfer efficiency achieved in the interior of these celestial bodies.

Interfaces and mixing, and beyond

Interfaces and mixing, and their non-equilibrium dynamics, govern a broad range of phenomena in nature and technology at astrophysical and at molecular scales. Supernovae and planetary convection, turbulence and turbulent mixing, combustion and chemistry-driven fluids, purification of water, and nanofabrication are a few examples. Addressing the societal challenges posed by alternative energy sources and the efficient use of nonrenewable resources requires an improved understanding of interfaces and mixing. Non-equilibrium dynamics of interfaces and interfacial mixing couples microscopic to macroscopic scales, and is a challenge to study in theory, experiments, and simulations. This special topic explores and assesses the state of the art in the non-equilibrium of interfaces and interfacial mixing, and charts new research directions in this actively developing area.

Bifurcations in rotating spherical shell convection under the influence of differential rotation.

The bifurcations of thermal convection in a rotating spherical shell heated from the inner sphere and driven by the buoyancy of a central gravity field are studied numerically. This model of spherical Rayleigh-Bénard convection describes large-scale convection in planets and in the outer zones of celestial bodies. In this work, the influence of an additionally imposed differential rotation of the inner sphere with respect to the outer one on the heat transfer and, more generally, on the whole bifurcation structure is investigated. In addition to numerical simulations, path-following techniques are applied in order to compute both stable and unstable solution branches. The dynamics and the heat transfer are essentially determined by a global bifurcation, which we have identified as a homoclinic bifurcation that consists of a collision of a stable modulated rotating with an unstable rotating wave.

A Model of Rotating Convection in Stellar and Planetary Interiors. II. Gravito-inertial Wave Generation

Abstract Gravito-inertial waves are excited at the interface of convective and radiative regions and by the Reynolds stresses in the bulk of the convection zones of rotating stars and planets. Such waves have notable asteroseismic signatures in the frequency spectra of rotating stars, particularly among rapidly rotating early-type stars, which provides a means of probing their internal structure and dynamics. They can also transport angular momentum, chemical species, and energy from the excitation region to where they dissipate in radiative regions. To estimate the excitation and convective parameter dependence of the amplitude of those waves, a monomodal model for stellar and planetary convection as described in Paper I is employed, which provides the magnitude of the rms convective velocity as a function of rotation rate. With this convection model, two channels for wave driving are considered: excitation at a boundary between convectively stable and unstable regions and excitation due to Reynolds stresses. Parameter regimes are found where the sub-inertial waves may carry a significant energy flux, depending upon the convective Rossby number, the interface stiffness, and the wave frequency. The super-inertial waves can also be enhanced, but only for convective Rossby numbers near unity. Interfacially excited waves have a peak energy flux near the lower cutoff frequency when the convective Rossby number of the flows that excite them are below a critical Rossby number that depends upon the stiffness of the interface, whereas that flux decreases when the convective Rossby number is larger than this critical Rossby number.

The effect of galactic chemical evolution on terrestrial exoplanet composition and tectonics

The increasing exoplanet catalogue of terrestrial to super-Earth sized rocky planets has necessitated approaches to address their surface conditions, degassing, tectonics, and habitability. One of the key unknowns is the spectrum of compositional endmembers, particularly in geophysically critical elements such as Fe (relative to Si), and heat producing elements (HPEs), including U, Th and K. The fractional distribution of these elements determines core size, gravity, and internal temperatures, which govern the geodynamics of rocky planets. Whilst the relative proportions of these elements can vary enormously in solar-system bodies, on long timescales, galactic chemical evolution (GCE) predicates the availability of these elements for building rocky planets. Existing models demonstrate a systematic dilution of heat producing elements over time, and an increase in Fe/Si due to increased Type Ia supernova activity since galaxy formation. Here we test the consequences of these trends for terrestrial planet behaviour. We assume an Earth-type planet – i.e., planets that accreted similarly to Earth, and inherited elements in a similar partitioning ratio as Earth to the Sun. We varied their Fe/Si ratios, and thus core size, and use a mineral physics package to calculate internal structures, physical properties, and gravity. Planets forming early in the Milky Way's history tend to have low Fe/Si ratios, and thus small cores, although elevated HPE budgets. The configuration of convection in planets that have large mantle fractions relative to the Earth tends to focus stress in the lithosphere and promote tectonic activity. Together with lower gravity, and thus weaker surface faults, plate tectonic behaviour is enhanced in small-core planets. In contrast, planets forming currently have higher Fe/Si, core size, higher gravity, and a lower propensity to plate tectonics. Our results imply a high-propensity for plate tectonics on Earth-sized planets early in galactic history, with the tendency for tectonics diminishing as the galaxy evolved.

A Model of Rotating Convection in Stellar and Planetary Interiors. I. Convective Penetration

Abstract A monomodal model for stellar and planetary convection is derived for the magnitude of the rms velocity, degree of superadiabaticity, and characteristic length scale as a function of rotation rate as well as with thermal and viscous diffusivities. The convection model is used as a boundary condition for a linearization of the equations of motion in the transition region between convectively unstable and stably stratified regions, yielding the depth to which convection penetrates into the stable region and establishing a relationship between that depth and the local convective Rossby number, diffusivity, and pressure scale height of those flows. Upward and downward penetrative convection have a similar scaling with rotation rate and diffusivities, but they depend differently upon the pressure scale height, due to the differing energetic processes occurring in convective cores of early-type stars versus convective envelopes of late-type stars.

Convection of a fluid with strongly temperature and pressure dependent viscosity

Plate tectonics on the Earth is a surface manifestation of convection within the Earth’s mantle, a subject which is as yet improperly understood, and it has motivated the study of various forms of buoyancy-driven thermal convection. The early success of the high Rayleigh number constant viscosity theory was later tempered by the absence of plate motion when the viscosity is more realistically strongly temperature dependent, and the process of subduction represents a continuing principal conundrum in the application of convection theory to the Earth. A similar problem appears to arise if the equally strong pressure dependence of viscosity is considered, since the classical isothermal core convection theory would then imply a strongly variable viscosity in the convective core, which is inconsistent with results from post-glacial rebound studies. In this paper we address the problem of determining the asymptotic structure of high Rayleigh number convection when the viscosity is strongly temperature and pressure dependent, i.e. thermobaroviscous. By a method akin to lid-stripping, we are able to extend numerical computations to extremely high viscosity contrasts, and we show that the convective cells take the form of narrow, vertically-oriented fingers. We are then able to determine the asymptotic structure of the solution, and it agrees well with the numerical results. Beneath a stagnant lid, there is a vigorous convection in the upper part of the cell, and a more sluggish, higher viscosity flow in the lower part of the cell. We then offer some comments on the possible meaning and interpretation of these results for planetary mantle convection.

A regime diagram of mobile lid convection with plate-like behavior

Terrestrial planetary bodies that undergo solid-state convection can exhibit a variety of tectonic styles, from stagnant lid one-plate planets to those with a mobilized lithosphere. For modeled planetary convection the de facto mode of recycling of lithosphere into the planetary interior is typically achieved through 2-sided and symmetric downwelling flows. However, lithosphere recycling on Earth occurs in a distinctly 1-sided mode known as subduction. Using numerical models of mantle convection in which the viscosity of planetary mantle material is strongly temperature-dependent, yet maintains a finite material strength as dictated by its yield stress, we investigate the continuum of mobile lid convection with plate-like behavior. The models span a parameter space of Rayleigh number and plate strength, and explore convective systems with low yield stresses resulting in weak subduction hinges that bend easily and highly deformable subducted slabs. Three distinct modes are found to occur in convective systems with weak plates: the stagnant lid mode, 2-sided downwelling mode, and a mode that alternates between 1-sided subduction and 2-sided downwellings. We classify the style of convective downwelling for a range of models and show that mode selection strongly depends on the combination of surface mobility and strength of the downgoing plate. Using these measurements, we have developed a regime diagram that can predict whether a particular system will be in one of those three modes.

El Niño as a consequence of the global oscillation in the dynamics of the earth’s climatic system

During study of the physical nature and potential precursor features of the El Nino phenomenon in the Pacific, it was found that a negative large-scale temperature anomaly on the Indian Ocean surface may be one of its significant precursors. This anomaly appears prior to the occurrence of El Nino and is accompanied by growth in atmospheric pressure. It gradually extends eastwards along the equator until the zone of planetary convection in the area of the Indonesian Region. The west wind that emerges on the eastern peripherals of the mentioned pressure anomaly leads to reversal of the Pacific segment of the Walker equatorial atmospheric circulation and to a subsequent change in the zonal thermal dipole polarity in the tropical zone of the Pacific (the latter means culmination of the El Nino phenomenon). In addition to the mentioned thermobaric anomaly in the Indian Ocean, other obvious signs of large-scale pressure anomalies have been found in the global atmospheric pressure field; these anomalies may be interpreted as manifestations of the intradecadal global oscillation in the dynamics of the modern climatic system. It is suggested that the whole known complex of events related to the El Nino phenomenon in the Pacific is a consequence and a regional link of the planetary structure of this global atmospheric phenomenon.

Model for hydromagnetic convection in a magnetized fluid

We consider convection in a horizontally magnetized viscous fluid layer in the gravitational field heated from below with a vertical temperature gradient. Following Rayleigh-Bénard scenario and using a general magnetohydrodynamic approach, we obtain a simple set of four ordinary differential equations. In addition to the usual three-dimensional Lorenz model a new variable describes the profile of the induced magnetic field. We show that nonperiodic oscillations are influenced by anisotropic magnetic forces resulting not only in an additional viscosity but also substantially modifying nonlinear forcing of the system. On the other hand, this can stabilize convective motion of the flow. However, for certain values of the model parameters we have identified a deterministic intermittent behavior of the system resulting from bifurcation. In this way, we have identified here a basic mechanism of intermittent release of energy bursts, which is frequently observed in space and laboratory plasmas. Hence, we propose this model as a useful tool for the analysis of intermittent behavior of various environments, including convection in planets and stars. Therefore, we hope that our simple but still a more general nonlinear model could shed light on the nature of hydromagnetic convection.

Some Aspects of Thermal Convection Theory for the Earth's Mantle

Summry A serious obstacle to developing a theory of the Earth’s thermal history, allowing for the possibility of convection, is the non-linearity of the convection equations. In particular, the non-linearity arising from viscosity variation with temperature is very marked. Instead of treating viscosity either as an adjustable parameter or assigning it some value derived from indirect observation, one would like to know what value it would assume from a consideration of convection theory itself, since this might largely determine the course of thermal history. Although an analytical approach to this is impossible, if one uses a reasonable hypothesis derived from Btnard cell experiments, an answer to this problem for the Upper Mantle can be suggested. The purpose of this paper is to draw attention to a few of the major problems that confront one in setting up a realistic theory of convection for the Earth‘s mantle and wh.ich are to a considerable extent a feature of any planetary convection theory. The first of these is in the nature of a brief reminder about the possibility of ever creating a self-contained theory of large-scale motions in the Earth‘s mantle. Although we do not have at present any direct observational data on long-term movements in the mantle, we have sufficient circumstantial evidence from crustal geology, vulcanology and seismology to make us believe that mantle and crustal motions occur over a very large range of length scales. We therefore have considerable a priori reasons for thinking that a complete theory of motions in the Earth’s interior will have a great complexity, comparable, perhaps with that for the atmospheric motions. As in meteorology one tries to break the total problem up into manageable pieces and what is normally described as a ‘ Theory of Mantle Convection ’ has its parallel in the problem of the general atmospheric circulation. However, this division of the problem raises a number of formal difficulties, which have their origin in the nonlinearity of the appropriate equations of hydrodynamics. This nonlinearity means that there is interaction between motions of all length scales and that a statement of initial and boundary conditions does not suffice to specify a theory of the motions within a limited length scale range. In the case of the atmospheric motions, which are more or less accessible to observation, a theory of motions within a restricted range of length scales has some prospect of success because it can be supplemented with empirical obFervations on motions outside the range of interest. Such observations would indicate how and to what extent the coupling of motions occur. In the absence of such detailed observational data, which is the situation with regard to mantle theories, it is an insoluble problem how to describe the interaction of large- and small-scale motions. What is more, unless there turns out to be a fairly well defined gap in the power spectrum of internal motions separating the largest scale motions of interest and the rest, the prospect of obtaining an adequate

Variations in planetary convection via the effect of climate on damage

A new model for the generation of plate tectonics suggests an important interaction between a planet's climate and its lithospheric damage behavior; and thus provides a simple explanation for the tectonic difference between Earth and Venus. We propose that high surface temperatures will lead to higher healing rates (e.g. grain growth) in the lithosphere that will act to suppress localization, plate boundary formation, and subduction. This leads to episodic or stagnant lid convection on Venus because of its hotter climate. In contrast, Earth's cooler climate promotes damage and plate boundary formation. The damage rheology presented in this paper attempts to describe the evolution of grain size by allowing for grain reduction via deformational work input and grain growth via surface tension-driven coarsening. We explore the interaction of damage and healing in two-dimensional numerical convection simulations. We also develop a simple “drip-instability” model to test the hypothesis that the competition between damage and healing controls convective and plate tectonic style by modulating episodicity at subduction zones. At small values of damage, f A , (or large values of healing, k A ) the lithosphere remains strong enough to resist subduction on time scales of billions of years. At intermediate values of f A and k A the lithosphere may become mobilized and allow for short bursts of tectonic behavior followed by periods of quiescence. At large (small) values of f A ( k A ) the fineness is increased so that the viscosity of the plate boundary is reduced to allow for continuous, unimpeded subduction of lithosphere and plate-like deformation. The results suggest the feasibility of our proposed hypothesis that the interplay of climate and damage control the mode of tectonics on a planet.

Round table discussion of session C: convection in planets and brown dwarfs

The following is an edited excerpt of the DVD recording of Session C's Round Table Discussion. Due to the tight publication schedule, participants have not been given much time to review its contents in detail. There may be unclear and inaccurate spots, but it should give an illustrative description of the dynamics of the interesting discussions.

Marginal stability of almost adiabatic planetary convection

Almost adiabatic states are typical for the deep convective interiors of all known planets and their moons, e.g., the deviations from the adiabatic state in the Earth's outer core and in the MHD dynamo region of Jupiter are about or less than 10−5%. We approximated the equations governing convection in the deep interiors of planets and their moons to obtain a system, which is more accurate than the traditional Boussinesq equations. Fortunately, our system, which adopts almost uniform entropy instead of the temperature as the basic thermodynamic states, can still be investigated by standard methods. We considered the marginal stability of well-mixed almost adiabatic states in rapidly rotating thick spherical shells, whose inner to outer radius ratio does not exceed that of the modern Earth. The critical Rayleigh-type numbers, frequencies and solution structures of the marginal states were determined by both analytical and numerical methods. Our new estimates differ from those obtained previously using the Boussinesq equations, suggesting that the earlier Boussinesq results for convection in the deep planetary interiors should be re-assessed. The small molecular Prandtl number limit was adopted to model the marginal stability of thermal planetary convection. It was found that the critical Rayleigh number for convection sharply diminished as the radius of the inner rigid core is increased. We modelled the instability of the combined compositional–thermal turbulent geo-convection for Prandtl number unity. When thermal convection is in opposition to compositional convection, extremely large critical Rayleigh numbers are possible. This might happen for a terrestrial planet during its later stage of evolution. Pure compositional convection has been investigated in the large compositional Prandtl number limit, for which the critical Rayleigh number is rather large and the variations of all critical parameters are small. The large size of the critical Rayleigh number ensures that the actual values used in numerical dynamo experiments are only moderately supercritical.

On the detection of pure sine waves embedded in a spectrum of stochastically excited p modes

The mode identification and fitting of solar oscillations provide an observational tool to derive the physical properties of the Sun’s interior. What has been devised for helioseismology can now be used for future asteroseismology ground-based instruments and space missions, such as the High-Accuracy Radial Velocity Planetary Searcher (HARPS) and Convection, Rotation and Planetary Transits (COROT). In the coming decade, numerous stars will be observed for which new tools will be needed. For instance, it is very likely that g and p modes will be detected, rendering the identification difficult. In addition, modes having both characteristics, known as mixed modes, are also likely to be detected in evolved stars; these latter modes are crucial for the understanding of the internal structure of the stars as they propagate deeply inside the stars, unlike the p modes. Unfortunately, the mixing will not only occur physically but also in the frequency domain: mixed modes will appear very close to stochastically excited p modes. In this paper, we have devised a new technique for detecting long-lived modes (mixed or g modes) embedded in a common p-mode spectrum. The technique has been validated using Monte Carlo simulations. In the framework of the hare-and-hound exercise of COROT, this technique has been applied to synthetic time series of the evolved solar-like star HD 57006. The results show that we can detect most of the mixed modes embedded by the hare. We also discuss the impact of how the long-lived modes are excited on the detection level. The technique described here can be applied to stars with a mass greater than 1.2 M� ,h a ving evolved possibly beyond the terminal-age main sequence, such as Procyon. Ke yw ords: methods: statistical ‐ stars: oscillations.

Zonal flow driven by deep convection in the major planets

The cause of the fast zonal winds on the large gas planets is disputed. To investigate their possible origin by convection in the planets' molecular hydrogen layer, I study simple numerical models of thermal convection in a rotating sphere at low Ekman numbers for Rayleigh numbers up to 100 times critical. With stress‐free boundaries and high Rayleigh number it is possible to reproduce the observed magnitudes of the zonal and non‐zonal flow components at the surfaces of Jupiter and Saturn. While only three flow bands are found for a thick convecting shell, the number increases to seven for a shell with an inner‐to‐outer radius of 0.6.

The influences of surface temperature on upwellings in planetary convection with phase transitions

The importance of surface temperature for mantle convection appears with the presence of adiabatic heating and cooling and the release and consumption of latent heat in the presence of phase transitions. For some planetary bodies these effects cannot be neglected. The dimensionless surface temperature T 0, which is the ratio between the temperature at the top of the convective region and the temperature drop across the mantle, is close to one for Mars and Venus. For the Earth, T 0 lies between 0.2 and 0.5. The dynamical influence of T 0 is especially poignant for internally heated convection with temperature-dependent viscosity. There is a tight coupling between the magnitude of the temperature field and the viscosity itself. We have studied temperature-dependent viscosity convection for both low- T 0 (0.2) and high- T 0 (1.2) situations and with internal heating in mantle convection with two upper-mantle phase transitions. Our results show that within this range of T 0 there exist two regimes for the evolution of upwellings in the mantle. In transient situations plume–plume collisions lead to the formation of megaplumes for high- T 0 regimes but are less likely to do so for low T 0. In the long-term regime, plumes with low T 0 are prone to develop from the transition zone with a supply of hot material coming from the shallow lower mantle. In systems with high T 0, however, long-lived plumes tend to have deeper mantle origins. In quasi-layered situations high T 0 may act as a positive feed-back mechanism in inducing powerful hot upwellings into the upper mantle.

Modelling planetary dynamics by using the temperature at the core–mantle boundary as a control variable: effects of rheological layering on mantle heat transport

In planetary convection, there has been a great emphasis laid on the usage of the Rayleigh number as a control parameter for describing the vigor of convection. However, realistic mantle rheology not only depends on temperature, pressure, strain-rate and composition, but also on the nature of the dominant creep mechanism, which varies with pressure and also with temperature. It is difficult to study the effects of varying influences from the convective strength without also changing the mantle flow law in the process. We have adopted the approach of using as the sole control parameter, the temperature at the core–mantle boundary, T CMB, in modelling planetary dynamics with a composite non-Newtonian and Newtonian rheology, which is temperature-dependent in the upper mantle and both temperature- and pressure-dependent in the lower mantle. Increasing the T CMB strengthens convective vigor and leads to a non-linear increase of averaged temperature, heat-flow and root-mean-squared velocity. The interior viscosity decreases strongly with T CMB and internal heating due to radioactivity. A viscosity maximum is found in the horizontally averaged viscosity profile at a depth around 2000 km. This viscosity hill moves downward with diminishing amplitude in the face of increasing dissipation number and internal heating. The bottom third of the lower mantle appears to be superadiabatic as a consequence of the stiff lower-mantle rheology. The scaling relationship between the Nusselt (Nu) number and T CMB shows a relatively insensitive increase of Nu with T CMB. In terms of an effective Rayleigh number of the whole system, Ra E, the power-law exponent of the Nu (Ra E) relationship is very low, around 0.12. Strong pressure-dependence of lower-mantle rheology and its large volume relative to the entire mantle would induce a much lower cooling rate of the planet than previous models based on parameterized convection with a temperature-dependent viscosity.

Spatial symmetry breaking in rapidly rotating convective spherical shells

Many problems in geophysical and astrophysical convection systems are characterized by fast rotation and spherical shell geometry. The combined effects of Coriolis forces and spherical shell geometry produce a unique spatial symmetry for the convection pattern in a rapidly rotating spherical shell. In this paper, we first discuss the general spatial symmetries for rotating spherical shell convection. A special model, a spherical shell heated from below, is then used to illustrate how and when the spatial symmetries are broken. Symmetry breaking occurs via a sequence of spatial transitions from the primary conducting state to the complex multiple‐layered columnar structure. It is argued that, because of the dominant effects of rotation, the sequence of spatial transitions identified from this particular model is likely to be generally valid. Applications of the spatial symmetry breaking to planetary convection problems are also discussed.