  Response modes computed via linear resolvent analysis of a turbulent
mean-flow field have been shown to qualitatively capture characteristics of the
observed turbulent coherent structures in both wall-bounded and free shear
flows. To make such resolvent models predictive, the nonlinear forcing term
must be closed. Strategies to do so include imposing self-consistent sets of
triadic interactions, proposing various source models, or through turbulence
modelling. For the latter, several investigators have proposed using the
mean-field eddy viscosity acting linearly on the fluctuation field. In this
study, a data-driven approach is taken to quantitatively improve linear
resolvent models by deducing an optimal eddy-viscosity field that maximizes the
projection of the dominant resolvent mode to the energy-optimal coherent
structure educed using spectral proper orthogonal decomposition (SPOD) of data
from high-fidelity simulations. We use large-eddy simulation databases for
round isothermal jets at subsonic, transonic, and supersonic conditions and
show that the optimal eddy viscosity substantially improves the alignment
between resolvent and SPOD modes, reaching over 90% alignment at those
frequencies where the jet exhibits a low-rank response. We then consider a
fixed model for the eddy viscosity and show that with the calibration of a
single constant, the results are generally close to the optimal one. In
particular, the use of a standard Reynolds-Averaged-Navier-Stokes (RANS)
eddy-viscosity resolvent model, with a single coefficient, provides substantial
agreement between SPOD and resolvent modes for three turbulent jets and across
the most energetic wavenumbers and frequencies.
