International Journal of Multiphase Flow 37 (2011) 1254–1255

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International Journal of Multiphase Flow

journal homepage: www.elsevier .com/locate / i jmulflow

Book Review

An Introduction to Gravity Currents and Intrusions, Ungarish, M.(2009). CRC Press, 489pp.

Gravity currents and intrusions occur whenever a fluid of onedensity flows primarily horizontally into a fluid of a different den-sity. Such flows are encountered in both natural processes as wellas in industrial applications, covering many different disciplines,ranging from Geophysical Science to Chemical Engineering. Thedynamics of these flows is often complicated by the presence ofparticles which contribute to the density contrast (e.g. in pipes,pyroclastic eruptions, avalanches); surface tension effects (as incavity flows or oil spreading in oceans); and chemical reactions(e.g. fire in tunnels and accidental release of toxic gases or liquids).Therefore, gravity currents and intrusions are multiphase flowswhich have been a subject of extensive fundamental research.

In particular, the field has received considerable attention overthe last 50 years, after the pioneering work of Abbott (1961) andthe famous paper of Benjamin (1968). Yet the only monograph de-voted to gravity currents worthy of note is that of Simpson (1987),re-edited 10 years later. Simpson’s book helpfully emphasizes theimportance of gravity currents and intrusions in geophysical andindustrial situations but is somewhat light on equations. Addition-ally, most of the newer findings are reported in papers dissemi-nated in different journals pertaining to various communities, sothat getting a unified vision of the main developments is a difficulttask. These circumstances make the present book, which is mainlydevoted to the description of theoretical models designed to repro-duce the dynamics of gravity currents, particularly timely. Amongothers, predictions of box-models, shallow-water approximations(to which a large emphasis is given) and Navier–Stokes equationsare presented and analyzed in the light of available experimentaldata.

The book is divided into two main parts of approximately equalsize corresponding to non-stratified and stratified ambients,respectively. Most of the situations considered are in the regimeof high-Reynolds number, except in two chapters (11 and 19) inwhich the contrasted configuration of viscous flows is tackled,using lubrication theory. After a short introductory section, theone-layer shallow-water (SW) theory is presented in chapter 2.This model and the two-layer extension described in chapter 5constitute the cornerstone of the book. In each case, analyticalsolutions of the model (including the constant-speed and self-sim-ilar phases) are given together with solutions of the full system ofequations by a finite-difference method. Reconciliation betweenBenjamin’s (1968) results obtained from a local analysis of thehead of a current spreading at steady-state, with time-dependentSW equations which consider the full body of the gravity currentis proposed in chapter 3.

Box-models are presented in chapter 4. In the case of planargravity currents, a careful comparison with the SW theory andavailable experimental and numerical data is performed. Such acomparison is repeated for axisymmetric configurations, buoyancy

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decaying currents and stratified planar/axisymmetric currents(including intrusions) in chapters 7, 9, 17 and 18, respectively.

As mentioned above, chapter 5 deals with the two-layer SWtheory. This chapter is particularly interesting for several reasons.First, it raises the issue of the choice of the model for the front con-dition, which is necessary for the closure of the SW equations. Theorigin, accuracy and relevance of each model are carefully ana-lyzed, and indications as to the most appropriate choice of modelare given for specific problems in the subsequent chapters. Sec-ondly, it clarifies the concept of ‘‘formal dissipation’’ which is aby-product of the SW model with respect to that of ‘‘real dissipa-tion’’ stemming from the irreversible loss of energy in a realsystem. Third, it alerts the reader to the ‘‘qualitative and quantita-tive differences between the shallow [i.e. lock-exchange configura-tion] and the deep ambient cases’’, and to the temptation toextrapolate results from the former case.

Chapters 6 and 7 extend SW and box-models to axisymmetricconfigurations, while interesting new phenomena, occurring whenthe system is in rotation, are presented in chapter 8. More complexmultiphase flows are investigated in chapter 9, namely particle-la-den flows and gravity currents spreading over porous media. Here,interesting perspectives regarding the modeling of the effects ofparticles on the motion of the current and vice versa are given,as illustrated by recent papers published in the International Jour-nal of Multiphase Flow (see e.g. Necker et al., 2002; Cantero et al.,2008). The approach presented in this book constitutes a goodstarting point from which more advanced models can beelaborated.

The Boussinesq approximation is been used in the book untilchapter 10 where the more general problem of non-Boussinesqflows is tackled. In these flows the relative density difference be-tween the current and the ambient is not negligibly small, say lar-ger than 30% or so. The non-Boussinesq one-layer SW modelpresented in this chapter is of particular practical interest sinceit allows for the description of both Boussinesq and non-Boussi-nesq currents, including light (top) currents and heavy (bottom)ones, in an unified framework. Note that the recently reportedtwo-layer extension of this model is not presented in the book(see Rotunno et al., 2011 and Ungarish, 2011, for lock-exchangeconfiguration and arbitrary initial fractional depths, respectively).I hope this model will be included in the next edition.

The second part of the book, dealing with stratified ambientconfiguration, roughly follows the same articulation as in the firstpart, that is SW equations in planar (chapter 12) and axisymmetricsituations (chapter 13) are given, including helpful analytical solu-tions (chapter 14). A new parameter, measuring the magnitude ofthe stratification, is included in the equations, and the validity ofthe models against possible physical interaction between the cur-rent and internal waves is discussed.

Depending on the local value of the density in the ambient withrespect to that in the current, the latter may spread as an intrusion.This specific problem is addressed in chapters 15 and 16. Here,

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both smooth (linear) and sharp (jump) stratifications are dis-cussed. As in the first part of the book, box-models are presentedand compared to SW theory, Navier–Stokes simulations and exper-imental data for stratified ambient in chapters 17 and 18, whilelubrication theory for viscous currents is given in chapter 19. Final-ly, chapter 20 ends the second and last part of the book by consid-ering the exchange of energy in horizontal gravity currents andintrusions.

The whole book is well written in a clear and pedagogical gen-eral style. The author sometimes calls the attention of the ‘‘carefulreader’’ to a specific subtle detail, making the reading of the bookinteractive.

For conciseness (the book is 489 pages long), the author delib-erately focused on simple planar and cylindrical geometries, whichis sufficient for the reader to comprehend most of the physical pro-cesses involved in the dynamics of gravity currents and intrusions.However, the case of gravity currents spreading along inclinedboundaries would have merited, in my opinion, if not a main part,at least a couple of chapters. Indeed, many of the applications arewith inclined boundaries, and the effect of inclination may be sig-nificant in some situations (Simpson, 1987).

Aside from this personal remark, the author has, in my opinion,produced the first comprehensive book entirely devoted to themodeling of gravity currents and intrusions. This book will be par-ticularly useful to graduate and PhD students, as well as to aca-demics and research engineers working in this field. It may beused as a self-consistent document to get a detailed idea of thestate of knowledge about a given problem or a guide toward morespecialized papers. It is rich with ideas regarding the direction inwhich further research is warranted. This book is ideal to get afirst, and yet deep, understanding of the dynamics of gravity cur-

rents and intrusions. From this understanding, one can investigateother related multiphase flow problems including surface tensioneffects, non-Newtonian behavior, porous media and chemical reac-tions, to name but a few.

References

Abbott, M.B., 1961. On the spreading of one fluid over another. Part ii. The wavefront. La Houille Blanche 6, 827–846.

Benjamin, T.B., 1968. Density currents and related phenomena. J. Fluid Mech. 31,209–248.

Cantero, M., Balachandar, S., Garcia, M., 2008. An Eulerian–Eulerian model forgravity currents driven by inertial particles. Int. J. Multiphase Flow 34, 484–501.

Necker, F., Härtel, C., Kleiser, L., Meiburg, E., 2002. High-resolution simulations ofparticle-driven gravity currents. Int. J. Multiphase Flow 28, 279–300.

Rotunno, R., Klemp, J.B., Bryan, G.H., Muraki, D.J. 2011 Models of non-Boussinesqlock-exchange flow. J. Fluid Mech. DOI: 10.1017/S0022112010006488.

Simpson, J.E. 1987 Gravity currents in the environment and the laboratory, EllisHorwood.

Ungarish, M. 2011 Two-layer shallow-water dam-break solutions for non-Boussinesq gravity currents in a wide range of fractional depth, J. Fluid Mech.DOI:10.1017/S0022112010006397.

Thomas BonomettiInstitut de Mecanique des Fluides de Toulouse,

UMR CNRS/INPT/UPS 5502,31400 Toulouse, France

Tel.: +33 5 34 32 29 52; fax: +33 5 61 28 59 91.E-mail address: thomas.bonometti@imft.fr