Two case studies
In this section we provide two examples of applications of the analysis methodology outlined earlier, focusing on the organised component of the turbulent jet discussed in the previous section; we also make use of the wavepacket sound source models of that section.
Let us begin by briefly recalling the analysis methodology: (1) we equip ourselves with complete or partial data from full Navier-Stokes solution; (2) we then identify the acoustic observable, qA, and design a corresponding filter, FqA , used to extract the radiating flow skeleton, qD; (3) we construct a simplified kinematic source model, s(qD) (based on the models developed in section §3), and verify that solution of Lqa = s(qD) is such that |qA — qA| be acceptably small. The final stage of the analysis methodology involves identifying the associated dynamic law; this aspect will be outlined briefly in section §6.
We use three different databases for the analysis, two LES and one DNS. The two LES use different numerical schemes, leading to one having higher space-time scale resolution than the other. We will refer to these as LESmd and LEShr, the subscripts denoting, respectively, moderate and high resolution. The DNS and LESmr therefore constitute databases where coherent structures are relatively easy to identify, on account, respectively, of the low Reynolds number and the moderate scale resolution. LEShR is more challenging, as it contains a broader range of turbulence scales, making the coherent structures more difficult to educe. In this case we are required to construct a filter based on Linear Stochastic Estimation (LSE).