Identifying the radiating core of Lighthill’s source term

A decomposition of the Lighthill source term is effected which yields ten sub-terms comprising velocity, vorticity, dilatation and density fields. An analysis methodology is then developed, aimed at understanding the respective roles played by these sub-terms in the production of sound. By Direct Numerical Simulation of a temporal mixing-layer—chosen both for its simplicity and its amenability to analysis in wavenumber space—the radiating components of the different sub-terms are isolated and studied. Interesting identities are observed between specific events in the evolution of the flow and the various sub-terms of the source, and the essence of the sound production mechanism is found to comprise subtle imbalances which disrupt inherent space–time symmetries which exist between the various sub-terms.

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