General considerations of the physics of planetary interiors

A deeper understanding of the constituents of the Solar System has been obtained over the last decade due primarily to the success of a variety of space missions which have provided a wealth of data to augment that obtained from Earth based observatories. Although the measurements refer directly to both the surface and atmospheric conditions, inferences can be made about conditions within the main bodies of the planets. This has been achieved through the closest collaboration between physicists, chemists and geologists in the study of these problems.In the present review we explore in a general way some of the types of problem involved with the physics of the interiors of planetary bodies. Concern will be with elucidating the structure of these bodies on the basis of the properties observed now. The arguments will be made in general terms and will not be concerned with any one planet in close detail.     

The significance of ferroelectric phase transitions for the Earth and planetary interiors

With the compelling evidence for orthorhombic perovskite ABO₃ structures in a major part of the earth's mantle, the question of whether any of these are ferroelectric (FE) or antiferroelectric should be of supreme importance. To answer this question the authors have conducted dielectric property studies at pressures up to 5.5 GPa on single crystals and polycrystalline aggregates of BaTiO₃ as well as other FE materials representing FE polarization mechanisms. The results indicate that: (1) h.p.-induced FE phases are indeed likely to play an important part in the earth's mantle; and (2) existing FE state, occuring as elastic and dielectric inhomogeneities, can persist to much higher pressures than expected on the basis of the pressure dependence of isolated and unclamped FE crystals. It is suggested that the presence of FE states in the earth's mantle may be responsible for some of its anomalous elastic and dielectric features, especially its attenuating properties. It is conjectured that effects of FE states on properties of the Jovian planets might even be more prominant, especially those involving dielectric constant and polarization.     

High-pressure studies of ferroelectric phases related to the earth and planetary interiors

To determine the effects of high-pressure constraints on the overall behaviour of ferroelectrics (FE) of both the perovskite “soft-mode” and hydrogen-bonded types, the authors have conducted dielectric property measurements to 5.5 GPa on single crystals and polycrystalline aggregates of several ferroelectrics (BaTiO₃, Pb(Zr,Ti)O₃, triglycine sulphate, Rochelle salt). The results of the experiments indicate: (1) dielectric hysteresis is possible in ferroelectrics which are under high-pressure conditions of deviatoric stresses and strains in which the FE phase forms part of a composite system; that is, under the conditions it would encounter if it formed part of a planetary interior; (2) the continued stability of these FE phases is not restricted to a particular polarization mechanism; (3) existing FE states, occurring as elastic and dielectric inhomogeneities, can persist to much higher pressures than expected on the basis of the pressure dependence of isolated and unconstrained FE crystals.     

Magnetohydrodynamics of stellar interiors

David Hughes, Robert Rosner and Nigel Weiss describe what was achieved during a programme on stellar magnetic fields at the Isaac Newton Institute in Cambridge. Over a four-month period more than 90 participants visited the Institute for a mixture of structured workshops and informal collaboration.     

Promoting planetary science

Mike Hapgood summarizes the RAS's position on planetary sciences in the UK, a subject that delivers world-class results, but needs focused support in order to continue to thrive.     

Displacement and rectification of planetary fluids

Abstract

Laboratory experiments on the decay (spin-up) of fluid motion on the β-plane are compared with theory. Under weakly dissipative conditions, some particles conserve potential vorticity during the entire decay. We also study the rectified mean flow which is produced by the lateral Reynolds Stress when a low frequency force is applied to the planetary fluid. The possible connection of effects with oceanic phenomena is briefly discussed.     

Generation of planetary magnetism by convection

Reliable measurements of the magnetic fields of Jupiter and Mercury have been obtained recently. Convection appears to be the most probable origin of Jovian and Hermaean magnetism as well as of geomagnetism. The similarity of the dynamo mechanism in the electrically conducting core of these planets offers opportunities for comparing different hypotheses and testing theoretical models. It is proposed in this paper that the realized magnetic field reaches a maximum amplitude in accordance with the dynamical constraints of nearly geostrophic motion and the condition for dynamo action.     

Long period divergent planetary waves

Abstract

A simple first order perturbation procedure is used to obtain an equation for divergent planetary waves when the period is much greater than the pendulum day. For unbounded regions the equation is the s2me as one derived by Longuet-Higgins (1965), but in bounded basins it is different. As an example, the eigen frequencies of a rectangular basin are calculated for a number of values of the parameters.

The energy density of planetary waves is also considered with results which correct those of Buchwald (1972) in the case of bounded basins.     

Solitary and cnoidal planetary waves

Abstract

A class of long planetary waves in a zonal channel analogous to the solitary and cnoidal waves of surface and internal gravity wave theory is discussed. On a mid-latitude β-plane, such waves exist as the result of divergence, non-uniform zonal velocity fields or bottom topography. In all cases studied the wave profile along the channel was found to satisfy the Korteweg-de Vries equation.     

加拿大行星地球科学研究进展

行星地质学和地球物理学(Planetary geology and geophysics,PG&G)是研究太阳系岩体和冰体表面与内部起源、结构和进化的科学.在过去几年中,加拿大地球科学家讨论并参与了一系列的行星科学研究,如对月球、火星和其他星体的研究,及参与探测宇宙飞船等研究.为此,《加拿大地球科学杂志》(Canadian Journal of Earth Sciences)发表特刊介绍加拿大科学家对行星地球科学的贡献.     

Heat transfer and planetary evolution

The object of this account is to show how much one can interprete and predict about the present state of material forming planet size objects, despite the fact we do not and could never have the kind of exact or prior knowledge of initial conditions and in situ material behaviour that would make a formal mathematical analysis of the dynamical problems of planetary evolution an efficient or meaningful exercise The interest and usefulness of results obtained within these limitations stem from the highly non linear nature of planetary scale heat transfer problems when posed in any physically plausible form. The non linearity arising from a strongly temperature dependent rheology assumed for in situ planetary material is particularly valuable in deriving results insensitive to such uncertainties. Qualitatively, the thermal evolution of a planet is quite unlike that given by heat conduction calculation below a very superficial layer, and much unnecessary argument and confusion results from a persistent failure to recognise that fact. At depths that are no greater on average than a few tens of kilometres in the case of Earth, the temperature distribution is determined by a convective flow regime inaccessble to the laboratory experimenter and to the numerical methods regularly employed to study convective movement. A central and guiding quantitative result is the creation in homogeneous planet size objects having surface temperatures less than about half the absolute melting temperature of their material, of internal states with horizontally a veraged viscosity values 10²¹ poise. This happens in times short compared with the present Solar System age. The significance of this result for an understanding of such processes and features as isostasy, continental drift, a minimum in seismic S wave velocity in Earth's upper mantle, a uniformity of mantle viscosity values, the survival of liquid planetary cores and the differentiation of terrestrial planet material is examined. After a discussion and definition of lithospheric material, it is concluded that endogenous tectonic activity only continues on Earth's surface on account of water enhancing the deformability of its rocks.Metal/silicate differentiation of terrestrial planet material is predicted to have been a global scale catastrophic process in the many objects it formed predating the existing planets, but intersilicate and volatile/silicate separations are necessarily protracted, quasi continous processes arising from local shear instabilties in the convective flow of such a viscous material. In particular, these local magma producing instabilities require the involvement of lithospheric planetary material in convective movements and it is shown how this unsteadiness accounts for the distribution and salient features of planetary seismicity and vulcanicity at the present time.The picture that emerges for the state of Earth's silicate shell material after more than four billion years of average viscosity regulation and shear instability is one of chemical and isotopic heterogeneity on a wide range of length scales. The larger length scales of this range are introduced by the pattern of heterogeneity remixing rather than its generation. For example, at the largest scale, the predicted heterogeneity is radial and a feature indirectly arising from properties conferred on the shell material by major mineral phase transitions at depths 700km. These increase the adiabatic temperature gradient and have the effect of a barrier adequate in strength to prevent wholesale mixing of the material above and below for at least a large fraction of the Earth's history in which radiogenic heat has been the dominant cause of large scale internal movements. That such a barrier actually marks a chemical and isotopic heterogeneity of the mantle is because only the convective movements above it are prone to the shear heating instabilities on which differentiation absolutely depends. Many millions of such instabilities in this shallower shell material would by now have created a three dimensional heterogeneity extending downward in length scale to 1km. However, only 10% of this shell material has yet experienced these highly localised shear heating instabilities and one would predict a continuing emission of primitive volatile phases and a widespread metasomatism even if the same convective movements had not recycled material from the hydrosphere. Such recycling is a further aspect of convective self regulation.The mesoscale and lateral heterogeneity of near surface material more familiarly referred to as continental crust and its underlying mantle is another cumulative feature of the remixing process-in this case the result of separated ultrabasic and less refractory fractions of the upper shell material from many shear heating events being able to form superficial blocks, whose net buoyancy and coherency make them immune to entrainment and remixing by the radiogenically driven flow. This partial but permanent concentration of lower melting point silicate and volatile phases near the external surface has in turn caused a gradual increase of the horizontally averaged temperatures associated with the self regulating convective state at upper mantle depths. This thermal evolution has strengthened the barrier to convective mixing of the whole silicate shell presented by its major phase transitions but it could explain a persistent small scale incorporation of more primitive, i.e. less differentiated shell material from the phase transition region into the upper shell convective circulation.Clear your mind of cant (Johnson)     

Are anharmonicity corrections needed for temperature-profile calculations of interiors of terrestrial planets?

It is shown that there is linearity between the thermal pressure P_TH and T between the Debye temperature θ and some high temperature $\text{T}{}^1$. $\text{T}{}^1$ has been measured at 1 atm and is reported for several minerals including, for example, MgO (1300 K) and forsterite (1200 K). The change in thermal pressure from room temperature for five solids, so far measured, indicate striking linearity with T at high temperatures.It is further shown that the value of $\text{T}{}^1$ increases greatly as the pressure increases. It is therefore concluded that P_TH is probably linear with T for mantle minerals under mantle conditions. The proportionality constant is derived from the measurements of thermal expansivity and bulk modulus at high temperature and zero pressure.The argument is then reversed. Assuming that the thermal pressure is in fact linear with T for the various shells in a planet, the resulting density and temperature profile of the planet is derived. The resulting density profile of the Earth compares favorably with corresponding values of recent seismic profiles.     

Periods of planetary waves in geomagnetic variations

Periods of planetary waves, especially the 10- and 16-day waves, were found in Fourier analyses of 10-year geomagnetic time series from two mid-latitude stations in the northern hemisphere. This suggests that planetary waves influence geomagnetic variations. Cross-spectral analysis of magnetic time series from seven stations located at around 50°N at the beginning of 1979, when a 16-day wave occurred in the stratosphere, also shows a 16-day oscillation. However, study of the phases does not reveal the horizontal direction of wave propagation. Furthermore, the temporal variations of the 16-day oscillation in magnetic time series are presented as dynamic spectra and the results are compared with global investigations of geopotential height data at 1 hPa (around 48 km) with respect to the 16-day wave for the same time interval. In some cases this comparison suggests a clear correlation between geomagnetic variations and planetary waves as well as a propagation of the 16-day wave up to the dynamo region (100-170 km).     

A numerical-physical planetary boundary layer model

A numerical-physical model for the planetary boundary layer has been formulated for the purpose of predicting the winds, temperatures and humidities in the lowest 1600 m of the atmosphere. An application of the model to the synoptic situation of 30 August, 1972, demonstrates its ability to produce useful forecasts for a period of 24 h. Results are illustrated in terms of horizontal maps and time-height sections of winds and temperatures. The model is divided in the vertical direction into three layers that are governed, respectively, by different physical formulations. At the lowest level, which is the surface of the earth, forecasts of temperature and humidity are computed from empirical relations. In the first layer, the surface layer, application is made of the similarity theories of Monin-Obukhov, Monin-Kazanski and Businger’s form of the universal functions. The second layer, the Ekman layer, is 1550 m deep and is governed by diagnostic momentum and time-dependent thermodynamic and humidity equations. External input to the model are large-scale pressure gradients and middle-level cloudiness. Cressman’s objective analysis procedure is applied to conventional surface and upper air data over a horizontal region of about 2500 km by 2500 km, centered about Lake Ontario. With a grid distance of 127 km and a time interval of 30 min, the computer time required on Control Data Cyber 76 for a 24 h forecast for the case study is less than two minutes.     

Traveling planetary waves in the stratosphere

This paper reviews the theory and observations of some traveling planetary waves in the stratosphere. Two categories of waves which appear prominently in the literature are discussed: westward propagating waves of periods in the range 3–7 days (the 5-day wave) and in the range 10–20 days (the 16-day wave). Although the observations seem to indicate that these waves are waves of the Rossby type (planetary waves), the evidence is less clear regarding (1) the question of whether these waves are forced internal waves or free (resonant) external waves, and (2) the identification of the observed waves with specific theoretical waves of the Rossby type. When recent observations are compared with theory, the evidence seems to favor the notion that the 5-day and 16-day waves of longitudinal wave number 1 may be identified, respectively, with the gravest and next gravest symmetric free Rossby modes. However, the observational evidence seems to be less clear regarding the nature of the 16-day wave than the 5-day wave.     

Quasi-free-decay magnetic modes in planetary cores

A new category of hydromagnetic waves in a rotating conducting fluid within a spherical shell geometry is investigated. These quasi-free-decay magnetic modes are based on particular solutions of the induction equation where the magnetic diffusion plays the central role. These solutions, normally only decaying with time, become propagative owing to the combined action of the background magnetic field and the rotation. The amplitude and sign of their azimuthal phase drift strongly depend on morphology and magnitude of the background magnetic field. The validity domain of these quasi-free-decay (QFD)-modes is related to the Elsasser number and is written as Λ???1. It follows that these modes dissipate quickly before propagating out. This restriction falls when the above criterion is no longer fulfilled (Λ?～?1), the corresponding modes evolving towards distorted QFD-modes. A systematic study of these QFD-modes is made in the limit of small Elsasser number (Λ???1), for the different symmetries allowed. Application to the Earth's and other planetary cores is then examined for an Elsasser number up to Λ?≈?O(1), in relation to the geomagnetic secular variation and the frozen-flux approximation.     

The planetary system and solar-terrestrial phenomena

Summary The Sun moves at different distances round the barycentre of the Solar System with different velocities depending on the distribution of the planets. The mean period of the Sun's motion round the barycentre of 11.8627 years and its time variability were observed. A relation between the basic period of 178.4 years and other periods p_i in the Sun's motion (p_i=178.4/i; i=1, 2, ...) was found. The consistency of the periods in the Sun's motion round the barycentre with the periods of different solar-terrestrial phenomena was studied. It seems that the planetary system governs these phenomena.

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Penetrative convection in the planetary mantle

Abstract

The hydrodynamic equations for thermal convection in a plane layer of viscous, heat conducting fluid are scaled using the normalization of Ostrach (1965) in which the magnitude of the non-dimensional group τ = gαd/c_p determines the importance of compression work and viscous dissipation in the energy balance of the flow. A linear asymptotic theory valid in the limit τ → ∞ is constructed for the Bénard problem and this is shown to be analogous to Couette flow between contra-rotating cylinders. For sufficiently large τ the flow becomes penetrative. This fact is illustrated for homogeneous fluids by the numerical integration of a set of coupled 1st order differential equations, both for the Bénard and internally heated configurations. The effect of viscosity and thermal conductivity in-homogeneity on the depth of penetration of the main cell in the circulation pattern are assessed and it is concluded that such interactions may be sufficient to effectively limit the depth extent of mantle convection. Finally a discussion of the effect of phase transitions is given following the technique of Busse and Schubert (1971).