Study of the linear models in estimating coherent velocity and temperature structures for compressible turbulent channel flows

Linear models, based on stochastically forced linearized equations, are deployed for spectral linear stochastic estimation (SLSE) of the velocity and temperature fluctuations in compressible turbulent channel flows with a bulk Mach number of 1.5. Through comparison with the direct numerical simulation (DNS) data, an eddy-viscosity-enhanced model (eLNS) outperforms the one not enhanced (LNS) in computing the coherence and amplitude ratio of streamwise velocity at different wall-normal heights, but they both largely deviate from DNS regarding the temperature prediction. For further investigation, the eigenspectra and pseudospectra of the linear operators are scrutinized. The eddy viscosity is shown to stabilize the eigenmodes and decrease the non-normality of the vortical modes. Consequently, the relative importance of acoustic and entropy modes increases, and they can contribute 20 % to 55 % of the response growth, which is not supported by DNS. Hence, it is an intrinsic defect of the eLNS model introduced by turbulence modelling. After a procedure of cospectrum decomposition, the contributions of acoustic and entropy components are filtered out. The resulting SLSE quantities for velocity, temperature and their coupling are basically agreeable with DNS, demonstrating that the coherent temperature fluctuation is dominated by advection and other vortical motions, instead of the compressibility effects. Moreover, a parameter study of Reynolds and Mach numbers (from 0.3 to 4) is conducted. The semi-local units are shown to well collapse the velocity SLSE quantities to the incompressible case for streamwise-elongated structures of high coherence.

Automated summary

Linear models and stochastic forced linearized equations are used for the estimation of velocity and temperature fluctuations in compressible turbulent channel flows. The eddy-viscosity-enhanced model performs better than the non-enhanced model in terms of coherence and amplitude ratio of velocity, but both deviate significantly from the direct numerical simulation (DNS) regarding temperature prediction. Analysis of the linear operators reveals that the eddy viscosity stabilizes eigenmodes and reduces non-normality of vortical modes, increasing the relative importance of acoustic and entropy modes. After decomposing the cospectrum, it is found that the coherent temperature fluctuation is dominated by advection and other vortical motions rather than compressibility effects. A parameter study of Reynolds and Mach numbers shows good agreement with the incompressible case for high coherence, streamwise-elongated structures.