Coherent pressure structures in turbulent channel flow

TL;DR

This study characterizes energetic coherent pressure structures in turbulent channel flows using spectral analysis and resolvent modeling, revealing dominant low-rank structures and mechanisms near vortices across different flow scales.

Contribution

It introduces a combined spectral proper orthogonal decomposition and resolvent analysis approach to identify and model pressure structures in turbulent flows, including the effects of eddy viscosity.

Findings

Strong dominance of leading SPOD modes for key structures

Resonance between resolvent modes and SPOD modes supports modeling approaches

Pressure fluctuations are primarily generated near vortex centers

Abstract

Most of the studies on pressure fluctuations in wall-bounded turbulent flows aim at obtaining statistics as power spectra and scaling laws, especially at the walls. In the present study we study energetic coherent pressure structures of turbulent channel flows, aiming at a characterization of dominant coherent structures throughout the channel. Coherent structures are detected using spectral proper orthogonal decomposition (SPOD) and modeled using resolvent analysis, similar to related works dealing with velocity fluctuations, but using pressure fluctuations as the output of interest. The resolvent operator was considered with and without the Cess eddy viscosity model. Direct numerical simulations (DNSs) of incompressible turbulent channel flows at friction Reynolds numbers of approximately 180 and 550 were employed as databases. Three representative dominant structures emerged from a preliminary spectral analysis: near-wall, large-scale and spanwise-coherent structures. For frequency-wavenumber combinations corresponding to these three representative structures, SPOD results show a strong dominance of the leading mode, highlighting low-rank behavior of pressure fluctuations. The leading resolvent mode closely agrees with the first SPOD mode, providing support to studies that showed better performance of resolvent-based estimators when predicting pressure fluctuations compared to velocity fluctuations. The dominant mechanisms of the analyzed modes are seen to be the generation of quasi-streamwise vortices with pressure fluctuations appearing close to vortex centers. A study on the individual contributions of the nonlinear terms (treated as forcing in resolvent analysis) to the pressure output reveals that each forcing component plays a constructive role to the input-output formulation, which also helps understanding the weaker role of forcing color in driving pressure fluctuations.