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**An introduction to gravity currents and intrusions.**
*(English)*
Zbl 1182.76001

Boca Raton, FL: CRC Press (ISBN 978-1-58488-903-8/hbk; 978-1-58488-904-5/ebook). xvii, 489 p. (2009).

Gravity currents and intrusions are common phenomena in nature, industry, and in the laboratory, where a fluid of one density flows horizontally into a fluid of different density. Understanding and predicting flow fields are important for both theory and practice. Written from the perspective of an applied mathematician or a theoretically oriented engineer, this book provides a comprehensive introduction to both the mathematical and physical aspects of this important topic. The material considered in this book is wide and has received considerable attention of researchers and engineers. The book aims at providing a solid foundation on which the researcher can build upon. The author has been admirably successful in presenting this monograph, with sufficient details but yet in a simple unified mathematical framework for the interpretation and prediction of gravity current flows. The theory is developed from the first principles and focuses on up-to-date methods and results with a wide range of applicability to apparent potential for further extensions.

A large part of the book is devoted to the study of motion in quite ordinary circumstances: currents which propagate on a horizontal surface, in systems of incompressible simple fluids, with small or moderate density differences, without special interfacial effects and with negligible interference with the “far end” boundary of the container. Complications introduced by inclined boundaries, interaction with obstacles, genuine three-dimensional geometries, underflow, inter-facial diffusion or chemical reactions, surface tension, non-Newtonian behavior, compressibility, and porous media are not considered, or are only briefly discussed. Exotic setups like a current in a converging wedge, or extreme cases like avalanches or a dam-break of a water reservoir in the atmosphere are also not considered. The simple systems which are the objectives of this book still display numerous ramifications which are followed in the text. These include two-dimensional and axisymmetric geometries, rotating and non-rotating frames, inertial and viscous reaction to driving forces, stratified and non-stratified ambient fluids, particle-driven flows, and more.

The book is divided into two parts: I. Non-stratified ambient currents; II. Stratified ambient currents and intrusions. The author has attempted to make the topics self-contained. This has necessitated some repetitions of definition, figures, scaling and conclusions.

Part I consists of 11 chapters. After an introduction to the subject, the subsequent chapters are related to: shallow water (SW) formulation for high-\(Re\) flows; the steady-state current and non-jump conditions; box model for 2D geometry; two-layer SW model; axisymmetric SW formulation; box model for axisymmetric geometry; effect of rotation; buoyancy decays (particle-driven, porous boundary, and entrainment); non-Bussinesq systems; and lubrication theory for viscous currents.

Part II concentrates on the topics: continuous density transition; axisymmetric and rotating cases; the steady-state current; intrusions in 2D geometry; intrusions in axisymmetric geometry; box models for 2D geometry; box models for axisymmetric geometry; lubrication theory for viscous currents; and energy.

Summarizing, the author, a recognized expert active in recent developments in gravity current research, has come out with an excellent book that provides an up-to-date, self-contained and systematic introduction to the study, interpretation, and prediction of gravity current flows. This accessible reference requires only a basic background in fluid mechanics and applied mathematics, making it an ideal starting place for researchers and engineers new to the field. The book is a welcome addition to the literature on gravity currents.

A large part of the book is devoted to the study of motion in quite ordinary circumstances: currents which propagate on a horizontal surface, in systems of incompressible simple fluids, with small or moderate density differences, without special interfacial effects and with negligible interference with the “far end” boundary of the container. Complications introduced by inclined boundaries, interaction with obstacles, genuine three-dimensional geometries, underflow, inter-facial diffusion or chemical reactions, surface tension, non-Newtonian behavior, compressibility, and porous media are not considered, or are only briefly discussed. Exotic setups like a current in a converging wedge, or extreme cases like avalanches or a dam-break of a water reservoir in the atmosphere are also not considered. The simple systems which are the objectives of this book still display numerous ramifications which are followed in the text. These include two-dimensional and axisymmetric geometries, rotating and non-rotating frames, inertial and viscous reaction to driving forces, stratified and non-stratified ambient fluids, particle-driven flows, and more.

The book is divided into two parts: I. Non-stratified ambient currents; II. Stratified ambient currents and intrusions. The author has attempted to make the topics self-contained. This has necessitated some repetitions of definition, figures, scaling and conclusions.

Part I consists of 11 chapters. After an introduction to the subject, the subsequent chapters are related to: shallow water (SW) formulation for high-\(Re\) flows; the steady-state current and non-jump conditions; box model for 2D geometry; two-layer SW model; axisymmetric SW formulation; box model for axisymmetric geometry; effect of rotation; buoyancy decays (particle-driven, porous boundary, and entrainment); non-Bussinesq systems; and lubrication theory for viscous currents.

Part II concentrates on the topics: continuous density transition; axisymmetric and rotating cases; the steady-state current; intrusions in 2D geometry; intrusions in axisymmetric geometry; box models for 2D geometry; box models for axisymmetric geometry; lubrication theory for viscous currents; and energy.

Summarizing, the author, a recognized expert active in recent developments in gravity current research, has come out with an excellent book that provides an up-to-date, self-contained and systematic introduction to the study, interpretation, and prediction of gravity current flows. This accessible reference requires only a basic background in fluid mechanics and applied mathematics, making it an ideal starting place for researchers and engineers new to the field. The book is a welcome addition to the literature on gravity currents.

Reviewer: Jagdish Prakash (Mumbai)

### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

76D50 | Stratification effects in viscous fluids |

76D33 | Waves for incompressible viscous fluids |

76D08 | Lubrication theory |

76B70 | Stratification effects in inviscid fluids |