A new insight into understanding the Crow and Champagne preferred mode: a numerical study

Abstract

The paper presents a new insight into understanding a mechanism to trigger the Crow and Champagne preferred mode. It is shown on the basis of numerical simulations that the preferred mode is established as a result of nonlinear interactions of primary structures generated by the Kelvin–Helmholtz instability. These interactions form larger coherent vortices characterized with frequency equal to half of the frequency of the primary perturbation. The paper shows that the shear-layer thickness at the nozzle exit constitutes a key parameter that influences significantly the jet response to an external forcing. The simulations were performed for jets with different shear-layer thicknesses. For the thicker shear layer the classical Kelvin–Helmholtz instability is observed. In this case the jet response to an external varicose forcing seems to be very similar to the experimental results of Crow and Champagne. The results presented shed new light on the preferred mode and the frequency selection mechanism confirming the suggestion of Crow and Champagne that nonlinearity is responsible for the preferred frequency. Significantly different results were obtained for a jet characterized by a thin shear layer. In this case the jet could be introduced into a self-sustained regime. External forcing with a frequency equal to the frequency of the natural self-sustained mode or with its subharmonic has practically no effect on the jet dynamics. The jet response to the forcing with frequencies different from the natural one depends on the forcing amplitude. A weak forcing disturbs the self-sustained mode leading to an interaction of two different modes that is observed in spectra with many frequencies related to both the self-sustained mode and the oscillations triggered by forcing. A stronger forcing suppresses the self-sustained mode and only the frequency components related to the stimulation are observed in the spectra. A mechanism responsible for the jet response to an external forcing under the self-sustained regime has not been extensively studied so far and a full understanding of these phenomena needs further studies and careful analysis.