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Double-diffusive convection. (English) Zbl 1301.76001

Cambridge: Cambridge University Press (ISBN 978-0-521-88074-9/hbk; 978-1-139-03417-3/ebook). xvi, 342 p. (2013).
The present book is, in fact, the first state-of-the-art review and selection of the best available approaches for describing double-diffusive convection. Important attention is also paid to the development of efficient numerical methods for solving partial differential equations, and to the parameter identification problem. The book consists of 13 chapters divided into three distinct parts. The first part (Chapters 1–5) presents the fundamental theory of double diffusion at a level suitable for a non-expert with some background in physical science. Chapters 6–9 present the discussion of flux laws, where the focus is on structures resulting from the primary double-diffusive instability – collective instability waves, intrusions and thermohaline staircases. The last part of the book (Chapters 10–13) explains the role of double diffusion in the broad context of environmental and physical sciences.
The chapters are as follows. Chapter 1: General principles; Chapter 2: The linear instability problem; Chapter 3: The unbounded gradient model; Chapter 4: The two-layer system; Chapter 5: The bounded layer model; Chapter 6: Collective instability; Chapter 7: Thermohaline intrusions; Chapter 8: Thermohaline staircases; Chapter 9: The unified theory of secondary double-diffusive instabilities; Chapter 10: Double diffusion in active environments; Chapter 11: Large-scale consequences; Chapter 12: Beyond oceanography; Chapter 13: Perspectives and challenges. The books ends with a huge list of 495 references and an index.
It is shown that the properties of vertical transport and the associated nonlinear dynamics depend on the geometry of the double-diffusive system, with specific examples presented in Chapter 3 for the unbounded gradient configuration, in Chapter 4 for the two-layer system, and in Chapter 5 for the vertical bounded layer model. Rather interesting is here Chapter 13. The author mentions here that “for an astrophysicist, the task of understanding a double-diffusive study in the oceanographic context may seem daunting at first, but a second look usually reveals that the differences in the way we approach the problem are rather superficial”.
In the reviewer’s opinion, the book provides a fundamental and comprehensive presentation of the mathematical and physical theory of double-diffusive convection, pointing out the most important practical applications. The complexity of the problems is gradually increased from very simple ones to problems for really intricate double-diffusive flows. The book is excellently written and readable. The numerical solutions of the considered problems are given graphically and in tabular form. The book will be useful to a wide range of specialists working in the area of double-diffusive convection.

MSC:

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76Rxx Diffusion and convection
76E06 Convection in hydrodynamic stability
80A20 Heat and mass transfer, heat flow (MSC2010)
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