Spectra of turbulent static pressure fluctuations in jet mixing layers

Spectral similarity laws are derived for the power spectra of turbulent static pressure fluctuations by application of dimensional analysis in the limit of large turbulent Reynolds number. The theory predicts that pressure spectra are generated by three distinct types of interaction in the velocity fields: a fourth-order interaction between fluctuating velocities, an interaction between the first-order mean shear and the third-order velocity fluctuations, and an interaction between the second-order mean shear rate and the second-order fluctuating velocity. In the inertial subrange the spectra associated with these three interaction modes exhibit k^-7/3, k^-9/3, and k^-11/3 power laws, respectively. Measurements of one-dimensional power spectra of the turbulent static pressure fluctuations in the driven mixing layer of a subsonic, circular jet are presented, and the spectra are examined for evidence of spectral similarity. Spectral similarity is found for the low wavenumber range when the large-scale flow on the centerline of the mixing layer is self-preserving. The data are also consistent with the existence of universal inertial subranges for the spectra of each interaction mode.