On Thermally Induced Sound Fields

Abstract

The sound fields induced in a real gas by boundary temperature variations are examined to illustrate how the pressure, temperature, and vorticity modes of motion interact. The pressure mode describes the irrotational propagation of longitudinal disturbances, the temperature mode, convective heat diffusion, and the vorticity mode, the diffusion of vorticity introduced at boundaries by the no-slip condition (boundary layer). The plane sound wave due to an instantaneous wall temperature rise is a sharp pulse, traveling at sonic speed and proportional to the inverse fourth root of the acoustic Reynolds number based on distance traveled; its thickness grows as the square root of elapsed time. Along a wall, it generates a boundary layer whose friction coefficient is proportional to the inverse square root of the acoustic Reynolds number based on distance from the front. The resulting effective wall slope induces a secondary circular pressure pulse generated by the foot of the plane wave; because this source moves at sonic speed, a pressure singularity appears there, due to the contributions piled up since the beginning of the motion.