1R38. Mechanics of Turbulence of Multicomponent Gases. Astrophysics and Space Science Library, Vol 269. - Edited by MYA Marov and AV Kolesnichenko (MV Keldysh Inst of Appl Math, Russian Acad of Sci, Moscow, Russia). Kluwer Acad Publ, Dordrecht, Netherlands. 2001. 375 pp. ISBN 1-4020-0103-7. $134.00.

Reviewed by AC Buckingham (Center for Adv Fluid Dyn Appl, LLNL, Mail Code L-23, PO Box 808, Livermore CA 94551).

This book provides both a valuable historical perspective and a comprehensive review of the theoretical considerations, model and procedural refinements, and illustrative computational results developed in Russia for analysis of terrestrial upper atmospheric physics and that of the atmospheric mantles surrounding the outer Solar System planetary giants. These planetary atmospheres are described as subject to nearly continuous molecular compositional, thermodynamic state and thermophysical phase changes as the result of, at least, the driving influences of: multi-spatial scale, compressible turbulent mixing; molecular mass, momentum, and energy transport processes; solar radiation absorption and transfer; buoyancy driven convective heating, ionosphere level electromagnetically driven charged particle accelerations; planetary atmospheric rotation, coupled global scale and local scale wind shear; and chemical reactions. The book is a monograph emphasizing nearly 30 years of the authors’ theoretical research and computational procedural development systematically combining these influences. Research was conducted by the authors, senior scientists and numerical procedure innovators, while at the MV Keldysh Institute of Applied Mathematics, Russian Academy of Sciences in Moscow.

The substantial reference list (over 350 sources) is usefully comprehensive particularly with respect to current published Russian work. Inadvertently, a few key non-Russian references outlining some important advances over the last 20 years in turbulence theory and simulation in the presence of reactive multicomponent species together with some information on high energy density experiments for astrophysical research applications are missing. Without implied criticism for the authors’ admirable and remarkable efforts in preparing this otherwise comprehensive book, but in the spirit of providing completeness for the reader, this reviewer has added some representative references to this later work in this review, specifically identifing the references, when added, with the reader’s attention drawn to a list of publications appearing at the end of this review. The cross index is useful, but somewhat sparse for the abundant topics and material developed. In particular, the reader may miss the inclusion of a combined topic and individual author cross-reference index with multiple entries.

The book is non-pedagogical in content, style, and organization. Consequently, it appears to have little use or appeal for student instruction. Its most probable appeal would be to specialists with interests in numerical modeling for analysis and evaluation of upper planetary atmospheric composition variation and dynamic structure. Another category of interested reader might be found in the non-specialist in atmospheric physics and fluid dynamics. This individual might be more fascinated with points made about the relative magnitude of the influence of the variety of physical processes, taken independently or in combination, that are considered in studies of the dynamics, thermodynamics and component composition of planetary atmospheres, or in chemically reactive compressible turbulent flows, generally.

The book is divided into two parts. The first part, consisting of five chapters, contains well over half of the book’s total content. It begins with an introduction and concise summary of the basic statistical fluid mechanics foundation of turbulence theory. The influence of turbulence is a central issue in its enhancement of molecular heat, mass and momentum transport processes in addition to its acceleration of molecular compositional changes through chemical reactions. The authors next move to discuss simplifications for modeling. This is in response to the need for practical emphasis on developing a simple closure model based on mean properties and localized in space; a model useful for evaluating the average influence of turbulence on the evolution of a concomitant physical process, rather than focusing on a deeper understanding of the nature of turbulence, a pursuit which while having academic appeal is fraught with potential disappointment.

First a single-point gradient transport level of modeling is adopted and the closure problem is systematically expanded and tested at the first order, algebraic level specifically limited for later comparison to a simple mixing length model. The next level of closure applied and tested involves what is called Reynolds stress closure. At this (2nd order) level, integral moment modeling is imposed. The undetermined correlations are linked (coupled) with transfer relations in the form of evolutionary (growth) differential equations, commonly identified as prognostic equations. These are numerically integrated in incremental steps over time to update the growth linkage variables to the next time interval. Emphasis is placed on the simultaneous upgrading of state and transport properties associated with the new time interval. Entropy balance and implicit onsager reciprocity are imposed as constraints to insure both equilibrium and irreversible thermodynamic consistency. Essentially, the authors develop and systematically describe the coupling of turbulent and background flow motion to underlying kinetic theory transport processes together with species production and phase changes. The unresolved turbulent scales of motion are determined using mean averaged single point turbulent gradient transport level modeling. Chemical reaction kinetics, driving species production and annihilation, are combined with kinetic theory considerations on the influence of diffusive transport, thermal conduction, and momentum transport (viscosity). The state dependent transport properties are developed separately from a kinetic theory approach (both the Chapman-Enskog expansion procedure and evaluated Boltzmann equation collision integral procedure are reviewed for developing the appropriate property values and thermodynamic state dependence).

As an added note, the reader’s attention is drawn to some substantial advances in more general turbulence closure theory and more detailed description of the turbulent small scale structure dynamics of direct interest in sub-grid scale modeling for recent progress in more detailed information using large eddy simulation (LES) procedures (Leslie 1), modeling the influence of turbulence at an average mean property level. Many new developments have appeared with respect to both theoretical and numerical investigations of the influence of compressibility on turbulence, an important component of generalized turbulent reacting flows. See for example the experimental and theoretical developments for free shear layer mixing and bounded shear layer mixing in quasi stationary turbulent supersonic flows (Smits and Dussauge 2). A good general review of compressibility influences on turbulence is also currently available for the reader (Lele 3). Considerable development in numerical simulations of turbulent reacting compressible flows is linked to the Beta probability density functional distribution for the reactive components in LES sub-grid scale modeling procedures simulating the influence of unresolved small scale turbulent mixing and coupled species production (Pope 4,5; Cook and Riley 6,7). While the importance of ocean-atmospheric coupling in the heat engine is a basic and as yet incompletely understood process in near surface atmospheric fluid dynamics studies (weather and climate modeling), attention in this book has been focused, necessarily on upper atmosphere and outer planetary mantle gas dynamical processes. However, for completeness the reader should be aware of some primary experimental and numerical studies in the terrestrial surface boundary layer and near surface atmosphere. For example, see Deardorff and Willis 8,9 as well as the recent review by Wyngaard 10.

The second part of the book is devoted to several illustrative applications of the computational procedures and comparison (where available) with experimental observations. The authors first present results and comparison of modeling coupled diffusive and photo chemical reactive species distribution and production in the upper atmosphere. Equivalent turbulent transport and scalar transfer coefficients for turbulent thermal diffusivity and dissipation are examined in conjunction with other turbulent parameter profiles from 90 to 120 km altitude. Presented results in the next chapter include comparing upper atmospheric turbulence generation with apparent fluctuations of the refractive index (observed as stellar light pulsations or scintillation and radio signal pulsations from distant space target sources. Planetary evolution processes for dust planetary disc coagulation undergoing turbulent heat and mass transfer are examined in the final chapter of the book.

Minor criticisms include finding a number of quite noticeable text typographical errors that slipped by in publication. For example, the fundamentally important Karman-Howarth equation of turbulent fluid dynamics which describes the growth, dissipation, and redistribution of turbulent kinetic energy over all spatial and temporal scales of motion appears as “Karman-Howart.” The unfamiliar label “balance” equations replaces the commonly accepted label “conservation” equations, and descriptive nouns and verbs such as “turbulization” and “turbulize” for the state and development of turbulence and “inviscous” for “inviscid” remain uncorrected or undefined in the text. A few errors of dimensional inconsistency (obviously typographical) may be found in the equations, such as that expressing the influence of the Lorentz Force in the upper atmospheric electromagnetic field.

Again, for completeness, the reader should be aware of recent work using a different approach (vortical dynamics) which seems to provide quite plausible atmospheric dynamic predictions for the Jupiter upper atmosphere mantle (Dowling 11). Stellar evolutionary processes with special attention to supernova events are receiving both numerical turbulent simulation and experimental attention currently. Here core radiation driven shock induced unstable mixing transition to turbulence and spatial development have also been addressed in experimental high energy density pulsed laser target interaction experiments, numerical simulation and theoretical scaling studies (Remington et al. 12, Robey et al. 13, Zhou 14).

The authors have written what should be an influential and certainly interesting chronicle summarizing almost three decades of theoretical model and numerical procedure development for use in basic upper atmospheric planetary research as well as use in evaluation and analysis of experimental evidence gathered for terrestrial and solar system investigations. The authors provide a systematic review of the mathematical foundation for their developments and an explicit derivation path to model assembly. They provide a lucid description of the physics issues that must be considered in providing a generally useful numerical model procedure for planetary atmospheric analysis. A major outcome and contribution is the development and illustrative test of a computational model for fully compressible turbulent, multi-phase, multi-component, chemically reactive flow. Mechanics of Turbulence of Multicomponent Gases is a tribute to the authors’ insight, innovativeness, and diligence as well as that of their Institute colleagues. The book also frames a moving memorial dedication to first author’s late wife who was also a principle scientific colleague and contributor, Senior Oceanographer, Natasha Marov. The book should prove to be a very desirable personal and library acquisition for atmospheric fluid dynamics and physics.

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