The effect of nonlinear interaction of instability eigenmodes on jet flow transition and its near acoustic field for a high-subsonic round jet at a Reynolds number of Re= 4.5ϫ 10 5 and a Mach number of Ma= 0.9 is investigated using large-eddy simulations. At the inflow, helical perturbations of azimuthal wavenumbers ͉n͉ = 4 , . . . , 8 determined from linear stability theory are superimposed on a laminar base flow in order to trigger transition to turbulence. The disturbance amplitude is varied parametrically in the range from 1.5% to 4.5% of the jet exit velocity U j . Thereby we aim to characterize sources of noise generation and, in particular, underlying mode interactions. With increasing forcing amplitude, the transitional behavior of the jet changes which affects the mean flow and also the acoustic near-field, which are both analyzed in detail. As the forcing amplitude is increased, the axial root-mean-square peak levels along the jet centerline are reduced by approximately 7%. Simultaneously, pronounced dual-peak distributions are generated along the jet lip line which are related to the localization of vortex pairings of the jet column mode. For low-amplitude excitation the azimuthal turbulent kinetic energy spectra show that the unexcited, naturally least stable axisymmetric mode n = 0 and the helical mode n = 1 dominate the early nonlinear regimes between z Ϸ 6r 0 and 9r 0 where r 0 is the jet radius. An analysis of the Fourier mode amplitude clarifies that this energy rise is linked to the helical mode n = 1. For higher forcing amplitudes, in addition to the varicose mode n = 0 interactions between the excited even mode n = 4 and higher azimuthal harmonics thereof dominate the azimuthal energy spectra. These differences in the early nonlinear development of the eigenmodes are found to alter the acoustic near-field. At small angles from the downstream jet axis, the peak acoustic frequency occurs at a Strouhal number based on the angular frequency and the jet diameter D j of St= D j / ͑2U j ͒ Ϸ 0.4. For low-amplitude forcing sound pressure levels are slightly enhanced which can be linked to the dominant low azimuthal wavenumbers identified in the transitional region. In the sideline direction, regardless of the excitation level, broadbanded spectra with maxima in the band 0.7 Յ StՅ 0.8 are found which is maintained at intermediate observer angles. For high forcing amplitude, however, a tonal component outside the initially excited frequency range is observed. This peak at StϷ 0.88 can be explained by weakly nonlinear interactions of initially forced eigenmodes n = 4 and n = 8 together with the jet column mode.

A wide range of flows of practical interest occur in cylindrical geometries. In order to simulate such flows, an available compact finite-difference simulation code [1] was adapted by introducing a mapping that expresses cylindrical coordinates as generalized coordinates. This formulation is conservative and avoids problems associated with the classical formulation of the Navier-Stokes equations in cylindrical coordinates. The coordinate singularity treatment follows [2] and is modified for generalized coordinates. To retain high-order numerical accuracy, a Fourier spectral method is employed in the azimuthal direction combined with mode clipping to alleviate time-step restrictions due to a very fine grid spacing near the singularity at the axis (r = 0). An implementation of this scheme was successfully validated by a simulation of a tripolar vortex formation and by comparison with linear stability theory.

Based on Lighthill's acoustic analogy we formulate the Spectral Lighthill Method (SLM). SLM is a method for the computation of acoustic far‐fields. It uses a spatio‐temporal Fourier transform of the Lighthill stress tensor. We show that SLM is a straightforward tool for the computation of acoustic far‐fields that enhances our physical understanding of sound generation and is useful in the numerical analysis of acoustic far‐field solvers. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A viscous stability code based on the linearized compressible Navier-Stokes equations in cylindrical coordinates was developed. In this contribution, we discuss general aspects of its application and present some results on the stability of swirling jet flow at high subsonic Mach number.

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