Identification of the Linear Sound Sources in Turbulent free Shear Flows: Non-modal Analysis and Direct Numerical Simulation Study
Acoustics
Final Report Abstract
The basic concept of our efforts is rooted in the breakthrough of the hydrodynamic stability community, after comprehensing the importance of the shear flow non-normality and mathematical description of the non-normality induced phenomena in the 1990s. This trend has been successfully adopted in atmospheric and astrophysical disk flow and within the fusion plasma communities. Non-normality induced phenomena are inevitable in shear flows, essentially changing the finite time period of the dynamics of the perturbations. At first, the shear flow non-normality leads to significant changes of the waves’ modal instability in the finite time period. Moreover, this brings forth a new type of linear phenomenon – the so-called vortex–wave mode coupling that ensures the emergence of quite strong wave harmonics subject to very specific initial characteristics. This linear vortex–wave mode coupling within the central part of time-developing shear layer is a dominant source in the generation of acoustic waves. The simplest “elements” of the linear dynamics are up-shear tilted (ky /kx > 0) vortex mode harmonics, that generate the related wave harmonics when crossing the ky = 0 line during the “drift” in spectral space. The key characteristic of the acoustic wave harmonics generation process are: • the dominance of 2D harmonics over 3D ones; • the increase of the efficiency of the wave generation with the increase of the streamwise length scale of the vortex harmonics; • the abrupt emergence of the wave harmonics from the vortex ones; • the regular/fixed phase of the wave harmonics at the moment of emergence (which is the basis of constructive interference of the linearly generated harmonics). Due to the large scale coherent structures in the layered turbulence, the linearly generated wave harmonics interfere constructively and form mostly 2D regular acoustic wave output: the greater the degree of coherence, the higher the regularity and strength of the wave output.
