Localized Resolvent-Mode Bases for Turbulence Statistics

Abstract

Modes from global resolvent analyses have been shown to accurately model the frequencies and spatial structure of the dominant coherent structures in several turbulent flows. However, resolvent-mode forcing models must be developed to predict the amplitude of the structures or other flow statistics, including the radiated noise. The present research aims to apply data-driven approaches to learn forcing coefficients from lower-order statistics available from Reynolds-averaged Navier-Stokes (RANS) predictions. As a first step towards this goal, we present a novel localized resolvent framework that reconstructs global quantities at low rank through spatially restricting the resolvent forcing and response domains. To illustrate the flexibility and robustness of the proposed framework, we initially utilize localized resolvent modes to reconstruct the spectral proper orthogonal decomposition (SPOD) modes of an isothermal Mach 0.4 jet at 𝑹𝒆 = 450, 000 = 450, 000. The results showcase the flexibility localized resolvent modes provide in the construction of global SPOD, while using 10 or fewer total localized modes total across 𝑺𝒕 = [0.05, 1.00]. Furthermore, we employ localized resolvent modes to reconstruct second-order statistics, comparing their performance with that of global modes. At low reconstruction error, it is shown that about twice as many global modes are needed to achieve comparable errors.

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