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ACOUSTIC RADIATIONS FROM LIGHTNING 59 seconds) come into dynamic equilibrium where the hydrodynamic drag force associated with their motion is balanced by the sum of all the externally expressed forces. When the electric field is quickly reduced by a lightning flash the cloud particles readjust to a new dynamic equilibrium. The change in the hydrodynamic drag force requires a change in the pressure distributions surrounding all the charged cloud particles; hence, the pressure in the volume continuing the cloud particles is altered by the sudden reduction of the electric field. Since the electric force from a charge concentration is outward, the pressure inside the charged volume will be slightly lower than the surrounding air. When E is reduced by the lightning flash the charged volume produces a slight implosion; this radiates a negative wave. Few (1982) derived a general expression for the internal pressure gradient produced by the electrostatic force; when integrated the result is In Eq. (4.9) the parameter n takes the value 0 for plane geometry, 1 for cylindrical geometry, and 2 for spherical geometry; P0 and E 0 are the values at the edge of the charged volume. The amplitude of this pressure signal is related to the electric field, the wavelength to the thickness of the charged region, and the directivity of the wave to the geometry to the source (Dessler, 1973). If the theory can be quantitatively verified, the signal can be used to determine remotely internal cloud electric parameters. The experimental search for electrostatic pressure waves has been difficult. The wave is low frequency (~ 1 Hz), small amplitude (~ 1 Pa), and buried in large background pressure variations produced by wind, turbulence, and thunder. Prior to Dessler's prediction of beaming, one wondered why the signal was not more frequently seen in thunder measurements. Holmes et al. (1971) measured a low-frequency component in a few of their power spectra of thunder but found these components completely missing in others. Dessler showed that that signal would be beamed for cylindrical and disk geometry; the disk case would require that the detectors be placed directly underneath the charged volume for observation. This relationship has been observed by Bohannon et al. (1977) and by Balachandran (1979, 1983). The electrostatic pressure wave predicted by the theory discussed above is a negative pulse. The measured acoustic signature thought to be the verification of the prediction actually exhibits a positive pulse followed by a negative pulse (see Figure 4.11). The negative pulse appears to fit the theory, but the theory is deficient in that the positive component of the wave is not described. Recently, Few (1984) suggested that the diabatic heating of the air in the charged volume by positive streamers may be the source of the positive pulse. Colgate and McKee (1969) described theoretically an electrostatic pressure pulse using this same mechanism but applied to a volume of charged air surrounding a stepped leader. This particular signature has not been experimentally verified because it has the regular thunder signal, which is 300 times more energetic, superimposed on it. ACKNOWLEDGMENT The author's research into the acoustic radiations from lightning has been supported under various grants and contracts from the Meteorology Program, Division of Atmospheric Sciences, National Science Foundation, and the Atmospheric Sciences Program, Office of Naval Research; their support is gratefully acknowledged. References Arnold, R. T. (1982). Storm acoustics, in Instruments and Techniques for Thunderstorm Observation and Analysis , E. 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