  The linear and mode-coupled contributions to higher-order anisotropic flow
are presented for Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 27, 39, 54.4,
and 200 GeV and compared to similar measurements for Pb+Pb collisions at the
Large Hadron Collider (LHC). The coefficients and the flow harmonics'
correlations, which characterize the linear and mode-coupled response to the
lower-order anisotropies, indicate a beam energy dependence consistent with an
influence from the specific shear viscosity ($\eta/s$). In contrast, the
dimensionless coefficients, mode-coupled response coefficients, and normalized
symmetric cumulants are approximately beam-energy independent, consistent with
a significant role from initial-state effects. These measurements could provide
unique supplemental constraints to (i) distinguish between different
initial-state models and (ii) delineate the temperature ($T$) and baryon
chemical potential ($\mu_{B}$) dependence of the specific shear viscosity
$\frac{\eta}{s} (T, \mu_B)$.
