A theoretical model of the shock wave from a lightning discharge ranging from the strong blast wave region out to the acoustic limit is given for the first time. The trajectory and overpressure of the strong shock wave are described by the well‐known equations for cylindrical blast waves. In the intermediate shock strength region (1.1 < M < 3.3), the shock trajectory is given by the ‘correct limit’ equation of Vlases and Jones. We derive an additional ‘correct limit’ equation for overpressure that is valid out to the acoustic limit. The correct limit equations predict a much slower decay of the intermediate shock wave; thus, the shock wave is much stronger at large distances from the discharge than was previously believed. Consequently, the range of action of the lightning discharge via its shock wave, as it affects the shattering and freezing of supercooled hydrometeors, may be large.

Equations for the trajectory and overpressure of the shock front of the intermediate strength blast wave (10 &lt; Δp/p0 ⪝ 0.02) are developed for spherical, cylindrical, and plane blasts. These equations are based on the correct limit method that provided the trajectory of the blast wave from the inverse pinch to velocities below Mach number 1.16 (Δp/p0 = 0.4). The correct limit equations are an extension of the strong shock similarity solution of G. I. Taylor for the spherical blast and A. Sakurai and S. C. Lin for the cylindrical case. It is now possible, given the energy and ambient gas conditions, to trace the shock front trajectory and overpressure from the very strong through the very weak regimes. Conversely, the shock wave energy can be found from measurement of overpressure or arrival time. Comparisons with experimental data as well as the calculations of H. L. Brode verify the validity of the correct limit equations.

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Similarity theory is used together with satellite data to estimate limits on the energy released by three solar flares. Bounds on the energy thereby distributed to the solar wind by satellite‐observed shock waves are 1030–1032 ergs for each of the flares. The blast‐like origin of these flares appears to be confirmed.

This study investigated the relationship of scores on the Psychopathic Deviate, Denial, Dependency, and MacAndrew Scales of the MMPI; intelligence; age; income; and education to continuance in a residential alcohol treatment program. Dropouts scored higher on the Psychopathic Deviate Scale than completers did. For completers, Psychopathic Deviate scores were correlated with age and Denial scores were correlated with intelligence. These relationships did not occur for dropouts. Findings were compared to research done in hospital settings.

IntroductionThe energy parameter B used in the strong blast wave equations is calculated for monatomic and diatomic gases. An application of the analysis of a cylindrical blast wave from an exploding wire is given.IV

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