Spectral proper orthogonal decomposition and resolvent analysis of near-wall coherent structures in turbulent pipe flows

Abstract

Abstract

Stochastic linear modes in a turbulent channel flow

“…As a reference, figure 5 represents the collinearity between SPOD and eddy resolvent analysis for all wavelengths at λ + t = 200 and λ + t = 1000 for Re τ = 180. It shows that, in agreement with the analysis of turbulent pipe flow by Abreu et al (2020b) (performed for ν-resolvent), the first ν t -resolvent mode predicts well the first SPOD modes for a wide range of wavelengths, especially for elongated modes (λ +…”

“…defined similarly as in Cavalieri et al (2013), Lesshafft et al (2019) and Abreu et al (2020b). As a reference, figure 5 represents the collinearity between SPOD and eddy resolvent analysis for all wavelengths at λ + t = 200 and λ + t = 1000 for Re τ = 180.…”

Forcing statistics in resolvent analysis: application in minimal turbulent Couette flow

“…Considering white-noise forcing, we can see some discrepancies in the amplitudes and in some details of the shapes of the streamwise vortices (v and w components). Despite acknowledging the origin of the forcing terms as arising from triadic interactions, resolvent analysis as formulated by McKeon & Sharma (2010) assumes white-noise forcing statistics, predicting thus streamwise vortices and streaks that are in reasonable agreement with the DNS, although with a mismatch in the relative amplitudes of u, v and w components; similar results were obtained for turbulent pipe flow by Abreu et al (2019). This will be explored in more detail in § 4.1.…”

“…In this framework, linear methods such as resolvent analysis (Jovanovic & Bamieh 2005;McKeon & Sharma 2010) and linear transient growth (Butler & Farrell 1992;Schmid & Henningson 2001) are useful to obtain optimal responses from the harmonically forced linearised Navier-Stokes system (resolvent) or the flow structure resulting from a non-modal growth of initial disturbances (linear transient growth). Both analyses, albeit linear, reproduce some experimental trends in both wall-bounded flows (del Álamo & Jiménez 2006;Pujals et al 2009;Abreu et al 2019;Morra et al 2019) and free-shear flows (Schmidt et al 2018;Lesshafft et al 2019). Nevertheless, there are intrinsic limitations to these approaches.…”

“…The present work focuses on exploring different forcing covariances and their effect on the covariance of the response. The first approach is to simply consider the forcing to be uncorrelated in space; for this case, previous analyses for wall-bounded flows has shown that even though reasonable agreement may be obtained for near-wall fluctuations (Abreu et al 2019), a mismatch is observed for large-scale structures (Morra et al 2019). One can also compute the nonlinear terms directly from a numerical simulation and then determine accurately P. If the simulation is converged and the signal processing is done properly, the result of (2.9) using the actual forcing covariance P (in the sense that this quantity is directly obtained from the simulation) should be equal to the response covariance S computed from the same simulation.…”