Allan D. Pierce
Dept. of Aerosp. and Mech. Eng., Boston Univ., 110 Cummington St., Boston, MA 02215
The propagation of sonic booms is from high above the ground to ground level, and over the path the dominant acoustic length scales in the signatures fall within what is known as the inertial subrange, for which there is a considerable body of basic theoretical knowledge. Any model of boom--turbulence interaction that requires a value for an outer scale has very weak theoretical basis. However, the range of turbulence scales within the inertial subrange is huge and different scales have different effects. The present paper argues that the turbulence can be split in a well-defined and logical manner, with the resulting scale at which the split occurs serving as an outer scale with respect to the turbulence that affects the rise times of sonic booms. Although molecular relaxation accounts for a substantial fraction of the rise times, the bulk of the thickening during daytime overflights is associated with turbulence. A theory for such thickening that simultaneously took both nonlinear steepening and turbulence into account had been proposed in the early 1970s by Plotkin and George, but had been criticized for its dependence on the choice of an outer scale. The proposed partitioning removes this objection and combines the salient ideas of Plotkin and George with others proposed by the author during the same epoch for the effects of inertial-subrange-scale turbulence on rise times.