It was a pleasure to read this important book. To understand and predict the development of turbulent flows represents both a continuing scientific challenge and also a serious practical problem in many different fields. Professor Pope has based his book on graduate level lecture courses on turbulence that he has presented at MIT and at Cornell University. It is intended for students in engineering, applied mathematics, oceanography and atmospheric sciences, as well as researchers and practising engineers. The emphasis is on turbulent flows, rather than on the theory of homogeneous turbulence, and only constant-density, nonreacting flows are considered. The author states that his aim is to explain concepts and develop the necessary mathematical tools, rather than to provide a practical guide to turbulence modelling. The text is divided into two parts. Part I provides an introduction to turbulent flows and the fundamental physical processes involved. Topics discussed in separate chapters include: the equations of fluid motion, the statistical description of turbulent flows, the mean flow equations, free shear flows, scales of turbulent motion and wall flows. The chapter on statistical methods for turbulence is particularly good; together with the related appendices it represents a valuable and accessible introduction to the subject. Several approaches for modelling or simulating turbulent flows are then described in Part II, in which the various chapters describe direct numerical simulation (DNS), turbulent viscosity models such as the k-ε model, Reynolds stress and related second-moment models, probability density function (pdf) models and large-eddy simulation (LES) techniques. Finally, some necessary mathematical tools are summarized in ten Appendices dealing with a wide range of relevant topics including tensors, Dirac delta functions, Fourier transforms, random processes, derivation of pdf equations, characteristic functions and stochastic descriptions of diffusion processes. I particularly enjoyed the chapters on modelling and simulation of turbulent flows. A unified treatment of the different types of model has enabled the author to make valuable connections between them and to reach clear and logical conclusions about the strengths and weaknesses of each approach. Over many years Professor Pope has made very important contributions to the development and application of pdf methods for the prediction of nonreactive and also reactive turbulent flows. The chapter on this subject is an exceptionally clear description of these powerful and often under-utilized simulation methods. The final chapter, on LES, provides an excellent introduction, with valuable and novel insights into both the promise and the problems of this relatively new and rapidly developing approach. It should be compulsory reading for many LES practitioners. Each section of the book contains a number of exercises, which typically invite the reader either to derive an expression that is quoted in the text or to generalize an analysis set out in the text. These exercises are often divided into several stages, and contain appropriate instructions, so that a diligent student will find his or her way through them. An advantage of the extensive use of appendices and student exercises is that analytical clarity and physical understanding are not obscured by unnecessary algebraic detail or by the need to review basic mathematical tools. The result is an exceptionally clear presentation, together with an often penetrating critique of both classical methods and recent developments in the theory and modelling of turbulent flows. There is excellent cross-referencing between one section and another, and an extensive and up-to-date bibliography. I strongly recommend this book to advanced students of fluid mechanics, to their teachers and to all researchers, engineers and others with a professional interest in turbulent flows. K N C Bray

Turbulent Flows: FUNDAMENTALS

Some Preliminary Thoughts * Part I: Inviscid Hypersonic Flow * Hypersonic Shock and Expansion-Wave Relations * Local Surface Inclination Methods * Hypersonic Inviscid Flowfields: Approximate Methods * Hypersonic Inviscid Flowfields: Exact Methods * Part II: Viscous Hypersonic Flow * Viscous Flow: Basic Aspects, Boundary Layer Results, and Aerodynamic Heating * Hypersonic Viscous Interactions * Computational Fluid Dynamic Solutions of Hypersonic Viscous Flows * Part III: High-Temperature Gas Dynamics * High-Temperature Gas Dynamics: Some Introductory Considerations * Some Aspects of the Thermodynamics of Chemically Reacting Gases (Classical Physical Chemistry) * Elements of Statistical Thermodynamics * Elements of Kinetic Theory * Chemical Vibrational Nonequilibrium * Inviscid High-Temperature Equilibrium Flows * Inviscid High-Temperature Nonequilibrium Flows * Kinetic Theory Revisited: Transport Properties in High-Temperature Gases * Viscous High-Temperature Flows * Introduction to Radiative Gas Dynamics.

Hypersonic and high temperature gas dynamics

A number of chemical-kinetic problems related to phenomena occurring behind a shock wave surrounding an object flying in the earth atmosphere are discussed, including the nonequilibrium thermochemical relaxation phenomena occurring behind a shock wave surrounding the flying object, problems related to aerobraking maneuver, the radiation phenomena for shock velocities of up to 12 km/sec, and the determination of rate coefficients for ionization reactions and associated electron-impact ionization reactions. Results of experiments are presented in form of graphs and tables, giving data on the reaction rate coefficients for air, the ionization distances, thermodynamic properties behind a shock wave, radiative heat flux calculations, Damkoehler numbers for the ablation-product layer, together with conclusions.

Review of chemical-kinetic problems of future NASA missions, II: Mars entries

Review of chemical-kinetic problems of future NASA missions. I: Earth entries

A practical polarization propagator method devised for the treatment of valence electron excitations in atoms and molecules is presented. This method, referred to as (second-order) algebraic-diagrammatic construction (ADC(2)), allows for a theoretical description of single and double excitations consistently through second and first order, respectively, of perturbation theory. The computational scheme is essentially an eigenvalue problem of a Hermitian secular matrix defined with respect to the space of singly and doubly excited configurations. The configuration space is smaller (more compact) than that of comparable configuration interaction (CI) expansions and the method leads to size-consistent results. The performance of the ADC(2) method is tested in exemplary applications to Ne, Ar and CO, where detailed comparison can be made with experiment and previous theoretical results. While the accuracy of the absolute excitation energies is only moderate, a very satisfactory description is obtained for the relative energies and, in particular, for the spectral intensities. Aspects related to the Thomas-Reiche-Kuhn sum rule and the equivalence of the dipole-length and dipole-velocity forms of the transition moments are discussed. Due to the relatively small computational expense and the possibility of a direct ADC(2) formulation this method should prove particularly useful in applications to large molecules.

https://iopscience.iop.org/article/10.1088/0953-4075/28/12/003/pdf

An efficient polarization propagator approach to valence electron excitation spectra

Radiative transport due to continua, molecular bands and atomic lines in inviscid nonadiabatic shock layer in stagnation region of blunt bodies

Radiative transport in inviscid nonadiabatic stagnation-region shock layers.

The spectral absorption cross section of the Swings band of C3 was determined from measurements behind incident shock waves that heated a gas mixture of argon and acetylene. These measurements spanned the spectral region between 300 and 540 nm, and were obtained at temperatures between 3200 and 4000 K. An electronic oscillator strength of 0.033 was deduced from the measurements.

An experimental determination of the cross section of the Swings band system of C3

An analysis of the radiative heating phenomena encountered during a typical aeroassisted orbital transfer vehicle (AOTV) trajectory was made to determine the potential impact of computational chemistry on AOTV design technology. Both equilibrium and nonequilibrium radiation mechanisms were considered. This analysis showed that computational chemistry can be used to predict (1) radiative intensity factors and spectroscopic data; (2) the excitation rates of both atoms and molecules; (3) high-temperature reaction rate constants for metathesis and charge exchange reactions; (4) particle ionization and neutralization rates and cross sections; and (5) spectral line widths.

Computational chemistry and aeroassisted orbital transfer vehicles

Electronic transition moments and their variation with internuclear separation are calculated for the Ballik-Ramsay (b 3 Sigma g - a 3 Pi u), Fox-Herzberg (e 3 Pi g-a 3 Pi u) and Swan (d 3 Pi g-a 3 Pi u) band systems of C2, which appear in a variety of terrestrial and astrophysical sources. Electronic wave functions of the a 3 Pi u, b 2 Sigma g -, d 3 Pi g and e 3 Pi g states of C2 are obtained by means of a self-consistent field plus configuration interaction calculation using an atomic basis of 46 Slater-type orbitals, and theoretical potential energy curves and spectroscopic constants for the four electronic states were computed. The results obtained for both the potential energy curves and electronic transition moments are found to be in good agreement with experimental data.

Theoretical electronic transition moments for the Ballik-Ramsay, Fox-Herzberg, and Swan systems of C2

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Radiative transport in inviscid nonadiabatic stagnation-region shock layers.

An experimental determination of the cross section of the Swings band system of C3

Computational chemistry and aeroassisted orbital transfer vehicles

Radiative transport in inviscid nonadiabatic stagnation-region shock layers.

Theoretical electronic transition moments for the Ballik-Ramsay, Fox-Herzberg, and Swan systems of C2