Localized resolvent-mode bases for turbulence statistics*

Global resolvent analysis modes have been shown to accurately model the frequencies and spatial structure of the dominant coherent structures in several turbulent flows. However, to predict the amplitude of the structures, or other statistics of the flow, resolvent-mode forcing models must be devised. The present research seeks to enable data-driven approaches to this problem by fitting the mode coefficients to match 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 breaks the resolvent forcing into a set of possibly overlapping spatial regions and reconstructs global quantities based on retaining the three highest-gain modes generated by the respective forcings. The localized modes are seen to provide a more flexible, robust basis by analogy with the general problem of approximating functions using global and local bases for both dominant and subdominant modes. By using the localized modes, lower-order flow statistics are reconstructed, such as Reynolds stresses, and compared to statistics computed using data from a large-eddy simulation.