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Noise measurements of heated axisymmetric jets at fixed supersonic acousticMach number indicate that the acoustic spectrum reduces when the temperatureratio increases. The `spectral quietening' effect has been observed bothexperimentally and computationally using Large Eddy Simulations (LES). It wasexplained by Afsar {\it et al}. (M. Z. Afsar and M. E. Goldstein $\&$ A. M.Fagan AIAAJ., Vol. 49, p. 2522, 2011) through the cancellation introduced byenthalpy flux/momentum flux coupling term using the generalized acousticanalogy formulation. But the parallel flow assumption is known to giveinaccurate predictions at high jet speeds. In this paper we therefore extendthe non-parallel flow asymptotic theory of Goldstein {\it et al}. (M. E.Goldstein, A. Sescu $\&$ M. Z. Afsar, J. Fluid Mech., Vol. 695, p. 199, 2012)for the vector Green's function of the adjoint linearized Euler equations(ALEE) in the analogy. Using a steady Reynolds Averaged Navier Stokes (RANS)calculation for the jet mean flow, we find that the coupling term propagator ispositive-definite and asymptotically sub-dominant at low frequenciescorresponding to the peak jet noise when non-parallel flow effects are takeninto account and self-consistent approximations for the turbulence structureare made. The validity of the non-parallel flow-based acoustic analogy model isassessed at various observation angles by computing the overall sound pressurelevel (OASPL) and use this to suggest a more rational explanation of thequietening effect. In general, our noise predictions are in very good agreementwith acoustic data beyond the peak frequency.

Effect of non-parallel mean flow on the acoustic spectrum of heated supersonic jets: explanation of `jet quietening'