The frequency dependence of jet turbulence for noise source modelling

The turbulence statistics of high speed jets provide a basis for modelling the source mechanisms responsible for noise generation. Progress in recent years where a statistical approach has been used includes better modelling of the subtler aspects of the turbulence field constituted by high speed jets, including anisotropy, inhomogeneity and the frequency dependence of the integral scales. In this paper, the frequency dependence of the length and time scales and the convection velocity are considered in order to provide improved turbulence models for the prediction of sound. It is shown that the use of a complex coherence function enables the frequency dependence of the turbulence scales to be established analytically. The frequency-dependent length scale is shown to be determined from the real part of this coherence function while the frequency-dependent time scale in the moving frame of reference is obtained from the modulus with the convection speed given by the phase. The results for the frequency dependence of the turbulence properties derived from two-point laser Doppler velocimetry measurements in high speed subsonic jets are presented and shown to agree well with those from an analytical model based on a Gaussian form for the two point correlation. The implications of the results in respect of noise prediction methodologies are discussed.