Robin O. Cleveland
David T. Blackstock
Appl. Res. Labs., Univ. of Texas at Austin, Austin, TX 78712-8029
Mech. Eng. Dept., Univ. of Texas at Austin, Austin, TX 78712-1063
Under certain conditions a finite-amplitude wave approaches a frozen state in which no further nonlinear distortion of the waveform takes place even though the wave amplitude would normally be regarded as still finite. Waveform freezing of sonic booms [W. D. Hayes and H. L. Runyan, Jr., J. Acoust. Soc. Am. 51, 695--701 (1971)], which is due to stratification of the atmosphere, is considered in this paper. The physical interpretation proposed is that stratification produces an effective coefficient of nonlinearity (beta)[sub eff] that approaches zero with travel distance. Most previous discussions of sonic boom freezing have been based on Hayes's ray theory computer program. Analytical predictions are reported here for both an isothermal model and a bilinear temperature profile model of the atmosphere. For straight downward propagation, which corresponds to a very high Mach number of the aircraft, the aircraft has to be at an altitude greater than 24 km (80 000 ft) for the boom to be within 5% of its frozen state when it reaches the ground. [Work supported by NASA.]