On the interaction between fundamental and subharmonic instability waves in a turbulent round jet

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Abstract
The spatial interactions between a fundamental instability wave and its subharmonics in a turbulent round jet are studied for ‘natural’ or forced exit conditions. Time-averaging and conditional-averaging techniques are used to split each flow component into a mean one, a random turbulence one and several wave-like coherent-structure components at fundamental and subharmonic frequencies. The energy equations for the flow components are derived and integrated across the jet. Shape assumptions regarding the radial distributions of each flow component are used to obtain a set of nonlinear ordinary differential equations representing the energy interactions between the coherent components, while interacting with the mean flow and with the background turbulence. Vortex pairing is viewed here as occurring when the subharmonic absorbs energy from the fundamental and from the mean flow and exceeds the fundamental's level to become the dominant instability component. At the proper initial phase difference between the subharmonic and fundamental only the first subharmonic was found to amplify if the fundamental Strouhal number based on diameter is in the range of 0.6–1.0. For higher Strouhal numbers, several subharmonics can amplify. The pairing location moves closer to the nozzle exit with increasing excitation Strouhal number. The time-averaged coherent Reynolds stresses exhibit regions of sign change, indicating a reversal in the direction of energy transfer between the mean flow and the coherent components.