The sound from mixing layers simulated with different ranges of turbulence scales

The role of turbulence scales in generating far-field sound in free shear flows is studied via direct numerical simulations of temporally developing, Mach 0.9 mixing layers. Four flows were simulated, starting from the same initial conditions but with Reynolds numbers that varied by a factor of 12. Above momentum thickness Reynolds number Re δ m ≈ 300 , all the mixing layers radiate over 85% of the acoustic energy of the apparently asymptotically high-Reynolds-number value that we are able to compute. Turbulence energy and pressure wavenumber spectra show the expected Reynolds number dependence; the two highest Reynolds number simulations show evidence of an inertial range and Kolmogorov scaling at the highest wavenumbers. Far-field pressure spectra all decay much more rapidly with wavenumber than the corresponding near-field spectra and show significantly less sensitivity to Reynolds number. Low wavenumbers account for nearly all of the radiated acoustic energy. Far-field streamwise wavenumber pressure spectra scale well with the layer momentum thickness, consistent with the insensitivity to Reynolds number of the largest turbulence structures. At higher wavenumbers the streamwise spectra scale best with the Taylor microscale. Interestingly, none of the spanwise far-field pressure spectra scale well with momentum thickness despite doing so in the near-field turbulence. Instead they scale well at all wavenumbers with the turbulence microscale. Implications of these results for large-eddy simulation of jet noise are discussed.