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Lectures on solar and planetary dynamos
PHYSICS OFTHE EARTH ANDPLANETARY INTERIORS
ELSEVIER
Physics of the Earth and PlanetaryInteriors99 (1997) 309-310
Book review Lectures on Solar and Planetary Dynamos, edited by M.R.E. Proctor and A.D. Gilbert, Cambridge University Press, Cambridge, UK, 1994, 375 pp., Hardback US$69.95, Paperback US$29.95.
At first I was reluctant to review this book because I have a strong negative bias against edited books; such books are often expensive and contain only one or two chapters in which I am interested. Fortunately, much to the credit of the editors, this book is an exception. The major goals of the book were to review the present state of knowledge of dynamo theory and to def'me the critical unsolved problems in the subject. To achieve these goals, the first seven chapters review various broad aspects of dynamo theory, while the last four chapters involve more specialized topics. For the most part the authors, all of whom are very well known for their contributions to dynamo theory, explain aspects of the theory in a pedagogical manner rather than selling a particular theoretical model that they favor. The typographical errors appear to be very rare, there is a bibliography associated with each chapter, and there is a general index. The first and longest chapter in the book was written by P. Roberts and reviews the basic concepts of dynamo theory. Roberts has a talent for this sort of undertaking and has an incredibly broad understanding of dynamo theory. I always learn something from reading a review by Roberts and this chapter proved to be no exception. Chapters 2 (by N.O. Weiss) and 4 (by Brandenburg) essentially deal with the solar dynamo. However, these chapters are not restricted to theory. Instead they review many of the observational data that must be explained by any viable theory; Weiss emphasizes the observations, while Brandenburg em0031-9201/97/$17.00 Publishedby ElsevierScienceB.V. PII S0031-9201 (96)03164-0
phasizes the computational side. For example, we learn from Weiss that the velocity field obtained by inverting helioseismological results differs from that obtained from the best computational models. We learn from Brandenburg that there is a serious problem in generating the 11 and 22 year solar cycles from numerical models: if the toroidal and poloidal magnetic fields are generated in the same regions, the change of rotation with depth in the convection zone is such that the solar cycles run in the opposite direction from observed. One possible solution to this problem is that the toroidal magnetic field is preferentially produced near the bottom of the convection zone and the poloidal magnetic field near the top. Sandwiched between these two chapters on solar and stellar dynamos is a chapter by Proctor dealing with convection and magnetoconvection in a rotating sphere. This chapter is not out of order but is fundamental to understanding several of the later chapters, including Brandenburg's. It is useful to try to understand convection in a non-magnetic system first, then in a system where a weak magnetic field is imposed, and finally in a system in which the magnetic field is strong (as measured by the ratio of the Lorentz force to the Coriolis force). Proctor does this well and establishes a solid foundation on which later chapters build. He ends with a brief discussion of instabilities. The fifth chapter is written by Malkus and is entitled "Energy Sources for the Geodynamo". However, only three pages of this chapter are devoted to thermal and compositional convection and even then references and understanding of recent work on this subject are essentially absent. Malkus pioneered the idea of a precession driven dynamo and it is this subject that he discusses here. Malkus primarily discusses the possibilities of tidal and precessional resonances. His arguments that these may
310
Book review
drive planetary dynamos are based on considerations of a few necessary conditions for dynamos and energy considerations; there is no discussion of how these resonances actually work to produce a dynamo. Nevertheless, even if they are not primarily responsible for producing a dynamo, they may, for example, play an important role in producing some of the phenomena observed in the geomagnetic secular variation spectrum. Thus, this chapter is well worth reading. Unfortunately, this also leaves an unfilled gap in the book dealing with alternative, and more mainstream, mechanisms for sustaining dynamos. The sixth chapter is on fast dynamos and is written by Soward, who appears to have established himself as the w o r d ' s leading expert on this subject. Fast dynamos are defined in the limit that the magnetic Reynolds number goes to infinity, i.e. diffusion effects can be ignored. In such dynamos the magnetic field grows exponentially on a convection time scale. As Soward reminds us, there is no evidence that fast dynamos exist anywhere in the universe. Unfortunately, this can give the incorrect impression that the study of fast dynamos may not have any practical uses. In reality, the study of fast dynamos can provide valuable insight into the induction process and possibly can provide bounds on some dynamo processes. Fearn does a superb job on Chapter 7 dealing with nonlinear planetary dynamos by rapidly getting to the heart of many of the controversial issues currently facing dynamo theoreticians. At center stage is the Taylor constraint - - a constraint that the net magnetic torque must vanish on the sides of any cylindrical surface in an inviscid fluid when the cylinder's axis is aligned with the rotation axis. Feam discusses dynamos that satisfy this constraint and ones that do not, such as model Z dynamos and dynamos in Ekman states. In the case of the geodynamo, the question of which state it is in essentially reduces to the strength of the viscous coupling between the mantle (and inner core) with the outer core. Fearn also has an illuminating discussion on
how mean field dynamos evolve between different states as the dynamo number is increased. He ends this chapter with a brief discussion of hydrodynamic dynamos. The final four chapters are on more specialized topics. In Chapter 8 Spiegel makes the case that the solar cycle is chaotic. In Chapter 9, Braginsky further develops the model Z dynamo that he pioneered. Braginsky has made numerous innovative contributions to dynamo theory in the past (for examples, MAC waves and convection driven by compositional buoyancy) and it may be unwise to ignore the many new insights into dynamo processes given in this chapter. Bayly introduces in Chapter 10 a new (at least to me) mapping technique for treating fast dynamos. Finally, in the last chapter Knobloch discusses bifurcations in rotating systems and provides a variety of interesting examples as to how one can still obtain valuable information on the nature of transitions without knowing many of the details of the problem. In summary, this is an excellent book that deals with the state of dynamo theory up to about early 1993. Unfortunately this means that some recent topics, such the role of the inner core in geodynamo theory, are barely mentioned. There are only a few gaps in the development. For example, although observational evidence from the sun is included, there is essentially no discussion of magnetic observatory, satellite, archeomagnetic or paleomagnetic data in this book. This means that there are no questions raised such as "are inversions of magnetic observatory data to obtain velocities near the top of Earth's core of use in dynamo theory?" However, such complaints are minor. The book would make an excellent choice to use in a graduate course on dynamo theory in an American University. In any case, anyone seriously interested in dynamo theory will want a copy in their personal library, RONALD T. MERRILL (Seattle, WA, USA)
ELSEVIER
Physics of the Earth and PlanetaryInteriors99 (1997) 309-310
Book review Lectures on Solar and Planetary Dynamos, edited by M.R.E. Proctor and A.D. Gilbert, Cambridge University Press, Cambridge, UK, 1994, 375 pp., Hardback US$69.95, Paperback US$29.95.
At first I was reluctant to review this book because I have a strong negative bias against edited books; such books are often expensive and contain only one or two chapters in which I am interested. Fortunately, much to the credit of the editors, this book is an exception. The major goals of the book were to review the present state of knowledge of dynamo theory and to def'me the critical unsolved problems in the subject. To achieve these goals, the first seven chapters review various broad aspects of dynamo theory, while the last four chapters involve more specialized topics. For the most part the authors, all of whom are very well known for their contributions to dynamo theory, explain aspects of the theory in a pedagogical manner rather than selling a particular theoretical model that they favor. The typographical errors appear to be very rare, there is a bibliography associated with each chapter, and there is a general index. The first and longest chapter in the book was written by P. Roberts and reviews the basic concepts of dynamo theory. Roberts has a talent for this sort of undertaking and has an incredibly broad understanding of dynamo theory. I always learn something from reading a review by Roberts and this chapter proved to be no exception. Chapters 2 (by N.O. Weiss) and 4 (by Brandenburg) essentially deal with the solar dynamo. However, these chapters are not restricted to theory. Instead they review many of the observational data that must be explained by any viable theory; Weiss emphasizes the observations, while Brandenburg em0031-9201/97/$17.00 Publishedby ElsevierScienceB.V. PII S0031-9201 (96)03164-0
phasizes the computational side. For example, we learn from Weiss that the velocity field obtained by inverting helioseismological results differs from that obtained from the best computational models. We learn from Brandenburg that there is a serious problem in generating the 11 and 22 year solar cycles from numerical models: if the toroidal and poloidal magnetic fields are generated in the same regions, the change of rotation with depth in the convection zone is such that the solar cycles run in the opposite direction from observed. One possible solution to this problem is that the toroidal magnetic field is preferentially produced near the bottom of the convection zone and the poloidal magnetic field near the top. Sandwiched between these two chapters on solar and stellar dynamos is a chapter by Proctor dealing with convection and magnetoconvection in a rotating sphere. This chapter is not out of order but is fundamental to understanding several of the later chapters, including Brandenburg's. It is useful to try to understand convection in a non-magnetic system first, then in a system where a weak magnetic field is imposed, and finally in a system in which the magnetic field is strong (as measured by the ratio of the Lorentz force to the Coriolis force). Proctor does this well and establishes a solid foundation on which later chapters build. He ends with a brief discussion of instabilities. The fifth chapter is written by Malkus and is entitled "Energy Sources for the Geodynamo". However, only three pages of this chapter are devoted to thermal and compositional convection and even then references and understanding of recent work on this subject are essentially absent. Malkus pioneered the idea of a precession driven dynamo and it is this subject that he discusses here. Malkus primarily discusses the possibilities of tidal and precessional resonances. His arguments that these may
310
Book review
drive planetary dynamos are based on considerations of a few necessary conditions for dynamos and energy considerations; there is no discussion of how these resonances actually work to produce a dynamo. Nevertheless, even if they are not primarily responsible for producing a dynamo, they may, for example, play an important role in producing some of the phenomena observed in the geomagnetic secular variation spectrum. Thus, this chapter is well worth reading. Unfortunately, this also leaves an unfilled gap in the book dealing with alternative, and more mainstream, mechanisms for sustaining dynamos. The sixth chapter is on fast dynamos and is written by Soward, who appears to have established himself as the w o r d ' s leading expert on this subject. Fast dynamos are defined in the limit that the magnetic Reynolds number goes to infinity, i.e. diffusion effects can be ignored. In such dynamos the magnetic field grows exponentially on a convection time scale. As Soward reminds us, there is no evidence that fast dynamos exist anywhere in the universe. Unfortunately, this can give the incorrect impression that the study of fast dynamos may not have any practical uses. In reality, the study of fast dynamos can provide valuable insight into the induction process and possibly can provide bounds on some dynamo processes. Fearn does a superb job on Chapter 7 dealing with nonlinear planetary dynamos by rapidly getting to the heart of many of the controversial issues currently facing dynamo theoreticians. At center stage is the Taylor constraint - - a constraint that the net magnetic torque must vanish on the sides of any cylindrical surface in an inviscid fluid when the cylinder's axis is aligned with the rotation axis. Feam discusses dynamos that satisfy this constraint and ones that do not, such as model Z dynamos and dynamos in Ekman states. In the case of the geodynamo, the question of which state it is in essentially reduces to the strength of the viscous coupling between the mantle (and inner core) with the outer core. Fearn also has an illuminating discussion on
how mean field dynamos evolve between different states as the dynamo number is increased. He ends this chapter with a brief discussion of hydrodynamic dynamos. The final four chapters are on more specialized topics. In Chapter 8 Spiegel makes the case that the solar cycle is chaotic. In Chapter 9, Braginsky further develops the model Z dynamo that he pioneered. Braginsky has made numerous innovative contributions to dynamo theory in the past (for examples, MAC waves and convection driven by compositional buoyancy) and it may be unwise to ignore the many new insights into dynamo processes given in this chapter. Bayly introduces in Chapter 10 a new (at least to me) mapping technique for treating fast dynamos. Finally, in the last chapter Knobloch discusses bifurcations in rotating systems and provides a variety of interesting examples as to how one can still obtain valuable information on the nature of transitions without knowing many of the details of the problem. In summary, this is an excellent book that deals with the state of dynamo theory up to about early 1993. Unfortunately this means that some recent topics, such the role of the inner core in geodynamo theory, are barely mentioned. There are only a few gaps in the development. For example, although observational evidence from the sun is included, there is essentially no discussion of magnetic observatory, satellite, archeomagnetic or paleomagnetic data in this book. This means that there are no questions raised such as "are inversions of magnetic observatory data to obtain velocities near the top of Earth's core of use in dynamo theory?" However, such complaints are minor. The book would make an excellent choice to use in a graduate course on dynamo theory in an American University. In any case, anyone seriously interested in dynamo theory will want a copy in their personal library, RONALD T. MERRILL (Seattle, WA, USA)