N. O. Weiss

Convection in the earth's mantle: towards a numerical simulation

Plate tectonics provides a remarkably accurate kinematic description of the motion of the earths crust but a fully dynamical theory requires an understanding of convection in the mantle. Thus the properties of plates and of the mantle must be related to a systematic study of convection. This paper reviews both the geophysical information and the fluid dynamics of convection in a Boussinesq fluid of infinite Prandtl number. Numerical experiments have been carried out on several simple two-dimensional models, in which convection is driven by imposed horizontal temperature gradients or else by heating either internally or from below. The results are presented and analysed in terms of simple physical models. Although the computations are highly idealized and omit variation of viscosity and other major features of mantle convection, they can be related to geophysical measurements. In particular, the external gravity field depends on changes in surface elevation; this suggests an observational means of investigating convection in the upper mantle.

An Active Sun Throughout the Maunder Minimum

Measurements of 10Be concentration in the Dye 3 ice core show that magnetic cycles persisted throughout the Maunder Minimum, although the Suns overall activity was drastically reduced and sunspots virtually disappeared. Thus the dates of maxima and minima can now be reliably estimated. Similar behaviour is shown by a nonlinear dynamo model, which predicts that, after a grand minimum, the Suns toroidal field may switch from being antisymmetric to being symmetric about the equator. The presence of cyclic activity during the Maunder Minimum limits estimates of the solar contribution to climatic change.

Sunspots : theory and observations

Preface. I: Introduction. The Theory of Sunspots J.H. Thomas, N.O. Weiss. II: Setting the Scene. Starspots P.B. Byrne. The Evolution of Sunspots C. Zwaan. III: Overall Structure of Sunspots. Continuum Observations and Empirical Models of the Thermal Structure of Sunspots P. Maltby. Observations of the Mesoscale Magnetic Structure of Sunspots A. Skumanich. Magnetohydrostatic Equilibrium in Sunspot Models K. Jahn. The Fate of the Heat Flux Blocked by Spots H.C. Spruit. IV: Fine Structure of Sunspots. Fine Structure of Umbrae and Penumbrae R. Muller. High Resolution Observations of the Magnetic and Velocity Fields of Simple Sunspots A.M. Title, Z.A. Frank, R.A. Shine T.D. Tarbell, K.P. Topka, G.B. Scharmer, W. Schmidt. Magnetoconvection M.R.E. Proctor. The Cluster Model of Sunspots A.R. Choudhuri. V: Waves and Oscillations in Sunspots. Sunspot Oscillations: Observations and Implications B.W. Lites. Magnetohydrodynamic Waves in Structured Magnetic Fields B. Roberts. Theory of Umbral Oscillations and Penumbral Waves S.M. Chitre. Sunspot Seismology: The Interaction of a Sunspot with Solar p-Modes T.J. Bogdan. VI: The Relation of Sunspots to the Global Solar Magnetic Field. The Formation of Flux Tubes at the Base of the Convection Zone D.W. Hughes. The Motion of Magnetic Flux Tubes in the Convection Zone and the Subsurface Origin of Active Regions F. Moreno-Insertis. VII: Concluding Summary. The Sunspot Phenomenon: A Commentary E.N. Parker. Index.

Two-dimensional Rayleigh-Benard convection

Two-dimensional convection in a Boussinesq fluid confined between free boundaries is studied in a series of numerical experiments. Earlier calculations by Fromm and Veronis were limited to a maximum Rayleigh number R 50 times the critical value R , for linear instability. This range is extended to 1000 R c . Convection in water, with a Prandtl number p = 6·8, is systematically investigated, together with other models for Prandtl numbers between 0·01 and infinity. Two different modes of nonlinear behaviour are distinguished. For Prandtl numbers greater than unity there is a viscous regime in which the Nusselt number

ON THE INTERACTION BETWEEN CONVECTION AND MAGNETIC FIELDS

N \approx 2(R/R_c)^{\frac{1}{3}}

Convective instability in a compressible atmosphere. II

, independently of p . The heat flux is a maximum for cells whose width is between 1·2 and 1·4 times the layer depth. This regime is found when

Dissipative heating in convective flows

5 \leqslant R/R_c \lesssim p^{\frac{3}{2}}

Periodic and aperiodic dynamo waves

. At higher Rayleigh numbers advection of vorticity becomes important and N ∞ R 0·365 . When p = 6·8 the heat flux is a maximum for square cells; steady convection is impossible for wider cells and finite amplitude oscillations appear instead, with periodic fluctuations of temperature and velocity in the layer. For p N ∞ R 0·365 , with a constant of proportionality equal to 1·90 when p [Lt ] 1 and decreasing slowly as p is increased. The physical behaviour in these regimes is analysed and related to astrophysical convection.

The solar tachocline

Turbulent convection in the solar photosphere can act as a small-scale dynamo, maintaining a disordered magnetic field that is locally intense. On the other hand, convection is inhibited in the presence of a strong, externally imposed magnetic field, as for instance, in a sunspot. Large-scale, three-dimensional, numerical experiments on highly nonlinear magnetoconvection in a Boussinesq fluid show that there is a continuous transition from a dynamo regime through a convective regime to an oscillatory regime as the strength of the imposed magnetic field is progressively increased. The patterns found in these different regimes are described and analyzed.

For how long will the current grand maximum of solar activity persist

The onset of steady convection in a polytropic atmosphere with constant viscosity is studied numerically. (AIP)