Pressure Disturbances of Impulsive Line Heat Sources

Abstract

The pressure disturbance produced by an impulsive line heat source is described. Physically, the line source may represent a lightning stroke and the pressure disturbance may represent the resulting thunder. The analysis begins with the Navier-Stokes equations, which describe flow in a compressible, heat-conducting, viscous medium. These equations are linearized and the flow is represented as the stun of a transverse and a longitudinal component. Laplace transforms are used to reduce the linear partial differential equations that describe the longitudinal flow to ordinary ones. These equations are solved for the Laplace transform of the velocity potential. The inverse transform is then obtained by approximation methods. Finally, the functional relation between the velocity potential and the pressure disturbance is derived and used to determine a description of the resulting sound wave. [This research was supported in part by the Weather Radar Branch, Meteorology Laboratory, U. S. Air Force Cambridge Research Laboratories, Office of Aerospace Research.]