On Spectra and Directivity of Jet Noise

Abstract

The present study develops a more quantitative picture of the relationship of jet noise to the turbulent structure of the jet. The work appears to predict qualitatively the changing directivity in different octave bands and at least in part the apparent paradox of a “reverse Doppler shift” of the spectrum peak. On the assumption of locally isotropic turbulence superposed on the mean jet flow, the broadly peaked noise spectrum is derived in terms of a sum of two bell-shaped spectra peaked an octave apart. The proportions vary with direction θ from the jet axis, being dominated by the “bass” spectrum at small angles and the “treble” spectrum beyond, say, 70°. This is accomplished by a factor ∼cos4θ for the “bass” spectrum. For small angles (e.g., 30°), points of the resultant curve are amplified (vertical shift) by convection of the eddies and “Doppler-” shifted (less than the full amount) in frequency. It is suggested that an increase in amplification toward the left may move the amplified peak in that direction. This could occur if, somewhat downstream of the potential core, the dominant noise emitters were located sufficiently close to the axis to be convected substantially faster than those in the mixing region.