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The book provides an excellent compendium of modern approaches to the Boltzmann equation and to techniques for obtaining exact solutions to approximate forms of the equation, or approximate solutions to the complete equation. Primary emphasis in the book is on the application of classical kinetic theory to the flow of monatomic neutral gases. The problems considered span the range of Knudsen numbers from continuum flow to free molecule flow. The solution techniques discussed include analytical solutions to model equations, moment methods, perturbation methods, variational methods, discrete velocity methods, and Monte Carlo methods. Of necessity, most of the discussion pertains to problems capable of being represented by a linearized version of the Boltzmann equation or model equation. Of particular interest is a complete chapter devoted to gas surface interactions and the implications of such interactions relative to boundary conditions for the Boltzmann equation. The book ends with a presentation of existence and uniqueness results for the Boltzmann equation. The bibliography is extensive and references pertinent material through 1974. The book should be of interest to all involved in solution of flow problems requiring the use of kinetic theory methods.

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The earliest results concerning the turbulence structure in a turbulent boundary layer with very unstable thermal stratification are due to Prandtl (1932). These results were developed further and made more precise by Obukhov (1946, 1960), Monin & Obukhov (1954) and Priestley (1954, 1955, 1956, 1960). All of these authors dealt with a surface layer of the Earth's atmosphere on hot summer days. Such a layer is the most easily accessible example of an unstably stratified boundary layer and it will be the main concern in this paper too. The theoretical predictions by the above-mentioned authors seemed at first to be confirmed by the available experimental data but in the late 1960s it became clear that at least some of the predictions disagreed strongly with the experimental information.A more elaborate theory was proposed by Betchov & Yaglom (1971) who used a suggestion of Zilitinkevich (1971). According to this theory, within an unstably stratified boundary layer there are three special sublayers where turbulence structure is self-preserving and obeys rather simple power laws. The new theory explained the disagreement between some of the deductions from the old theory and the data. However, the data available in 1971 were insufficient for the confirmation of the new theory and it was even supposed by Betchov & Yaglom (1971) that their theory could not be applied to atmospheric surface layers on hot summer days.Much new experimental data concerning unstably stratified boundary layers has been obtained in recent years; in particular, extensive experimental information was collected during the summers of 1981–1987 at the Tsimlyansk Field Station of the Moscow Institute of Atmospheric Physics. This paper is a survey of the deductions from the theory by Betchov & Yaglom which concern the mean fields and the one-point fluctuation moments in unstably stratified boundary layers, and a comparison of these deductions with the data available in 1989. It is shown that the data agree more or less satisfactorily with the theoretical predictions and permit one to obtain estimates for a number of coefficients that enter the theoretical equations.

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