Linear Stability Analysis of Round and Serrated Jets

We investigate the velocity and pressure fluctuations of turbulent jets produced by round, and serrated nozzles. We model these fluctuations via the normal modes of the linearized equations and derive a generalized Rayleigh-equation for mean-flows composed of an arbitrary number of azimuthal harmonics, allowing fast solution of both the temporal and spatial stability problems. Using ensamble-averaged turbulent mean-flows from stereoscopic PIV data, we solve the generalized Rayleigh-equation and compare our predictions to instantaneous PIV measurements as well as near-field microphone measurements. Using the proper orthogonal decomposition to filter out uncorrelated fluctuations in data, we find good agreement between data and theory.