Time-domain modeling of the wind effects on the nonlinearity and absorption of sonic booms

Abstract

This paper discusses the derivation and solution, in the time domain, of a Burgers’ equation for sonic boom propagation in a windy atmosphere. As the wind effects become important with increasing wind speed, the proper treatment of wind is necessary for sonic booms propagating through a jet stream as well as for those propagating to the stratosphere or thermosphere where stronger winds typically exist. The effects of wind are quantified in terms of the Doppler shift and of a parameter which measures the strength of the convection. The latter, referred to as the convective index, is a ratio of the local sound speed to the magnitude of the ray velocity and is unity in the absence of wind. Both Doppler shift and convective index are larger than unity if there is a component of the wind velocity opposite to the direction of the acoustic propagation. Consequently, the effective nonlinearity coefficient and effective absorption coefficients are larger for rays propagating opposite the wind direction than for rays propagating in the same direction. To demonstrate the significance of the derived Burgers’ equation, the effect of a jet stream with a typical strength and profile on nominal sonic booms will be described.