A numerical investigation of the thickening of a shock wave on passing through turbulence

Abstract

The characteristic 'N' shaped pressure waves recorded at ground level below the flight path of supersonic aircraft have compressive regions very much less steep than predicted by theory, with a consequent reduction in the subjective annoyance. Attempts have been made to explain this phenomenon in terms of the effect of atmospheric turbulence. This Report is concerned with the particular proposal that since on passing through turbulence a shock will tend to become thicker for part of the time and to steepen for the remainder then if the thickening process operates faster than the steepening a net increase in thickness will result. The problem is simulated in one-dimension by a variation of the 'piston problem' in which pressure waves representing turbulence are made to pass through a shock wave. The governing partial differential equations are solved using a finite difference technique. The results of the calculations show that a shock wave tends to become thicker on passing through a disturbance wave having equal positive and negative parts. This is consistent with the proposed explanation of shock-thickening although the thickening calculated is small compared to the initial shock thickness, for the disturbance waves used. Distortion of the disturbance waves with time prevented a wider study of the effects of varying amplitude and wavelength being made so that precise quantitative conclusions could not be drawn but it is suggested that the process investigated is unlikely to be powerful enough to produce the shock thickening measured experimentally in sonic boom research.