Introduction to modeling convection in planets and stars. Magnetic field, density stratification, rotation (Q2863827)

This book provides readers with the skills they need to write computer codes that simulate convection, internal gravity waves and magnetic field generation in the interiors and atmospheres of rotating planets and stars. It is very useful for readers having a basic understanding of classical physics, vector calculus, partial differential equations, and simple computer programming. The topic of parameterized convection, necessary for mixing-length theory, hydrostatic circulation models, and mean field models of dynamo theory is not considered in the book.NEWLINENEWLINEWho can summarise the contens of this excellent textbook better than the author. Here we give parts of his preface to the work:NEWLINENEWLINE``Part 1 of the work (chapters 1-7), ``The Fundamentals'', reviews the concepts and equations of thermal convection, and then it describes, step by step, how to design a computer program that employs basic numerical methods for solving these equations to simulate convection in a 2D cartesian box of fluid heated from below. Internal gravity waves can be simulated by simply reversing the thermal boundary conditions. By prescribing a stable thermal stratification in part of the fluid domain and an unstable stratification in another part one can simulate a combination of gravity waves and convection. Double-diffusive convection is also a combination of gravity waves and convection; it occurs when buoyancy is due to perturbations in both temperature and composition with the secondary constituent of the fluid being much less diffusive than temperature. The numerical method presented in this part to simulate these types of dynamics is spectral in the horizontal direction and finite difference in the vertical direction, which introduces the reader to these two very different methods. The linear stability problem is first addressed, which provides readers a way to check their time-dependent linear program. Then, the nonlinear terms are added to produce numerical simulations. I have chosen the Galerkin method to calculate nonlinear terms so readers gain a better understanding of how energy cascades between spatial scales; a more efficient (spectral-transform) method is described in Part 2. Graphical analyses of the simulated data, including making movies, is also discussed in Part 1.NEWLINENEWLINEPart 2 (chapters 8-10), ``Additional Numerical Methods'', describes alternative numerical methods that improve accuracy and efficiency and provide more realistic geometry. For example, semi-implicit, instead of explicit, time integration schemes are presented; fully finite-difference and fully spectral methods are discussed; the spectral-transform method for calculating nonlinear terms, instead of the Galerkin method, is described; and a local cartesian geometry is converted into global 2D, 2.5D, and 3D spherical shell geometries. For efficiency, I include magnetic, density stratification, and rotational terms and equations in the discussion of the numerical methods for 2.5D and 3D spherical shell convection in Section 10.6 before formally introducing these physical effects in Chapters 11-13. The reader could simply choose to ignore these extra terms until they are needed in Part 3 of this book or could read the introduction to Chapters 11-13 before proceeding through Section 10.6.NEWLINENEWLINEPart 3 (chapters 11-13), ``Additional Physics'', reviews the effects of magnetic fields, density stratification, and rotation. Chapter 11 (Magnetic Field) does not require any of the material in Part 2; therefore readers who are interested in adding magnetic field to the model described in Part 1 can go directly to Chapter 11. The linear analyses and nonlinear simulations with these additional physical effects are described in detail for 2D simulations; they are also described for 2.5D and 3D in Chapter 13, including two standard benchmarks for global 3D convection dynamos. In the final section (13.7) I list several more sophisticated computer modeling features of planetary and stellar convection that are beyond the scope of this book.'' (Glatzmaier, Preface, pp.\ xi, xii).NEWLINENEWLINEThus, the focus of Part 1 and most of the applications of the Parts 2 and 3 is directed to two-dimensional models, because 2D-models are simpler to write and require far fewer computational resources. As applications double-diffusive convection like in an ocean (salt in water), a magmatic chamber (MgO in a magmatic melt), or in a giant planet or star (heavy elements in hydrogen) are discussed. Besides, thermal convection within the mantle of terrestrial planets (Section 8.4), convection in systems with open boundaries as planetary and stellar atmospheres (Section 10.1), magnetoconvection with an arbitrary magnetic background field (Section 11.6), nonlinear anelastic simulations (Chapter 12), axisymmetric simulations with flows and fields varying within a meridional plane, and 3D rotating spherical-shell magnetohydrodynamic dynamo models, e.g.\ for Saturn (Section 13.5), are considered.NEWLINENEWLINEEvery chapter contains exercises asking, for instance, the reader to derive mathematical results presented in the text. To apply the newly obtained knowledge, suggested computational projects require the development of small programs by the reader himself. Computer graphical movies of some of the programs described or derived in the book are available via the book's web page at {\texttt{http://press.princeton.edu/titles/10158.html}}.