  One of the long-standing problems in the field of high-energy heavy-ion
collisions is that the dynamical models based on viscous hydrodynamics fail to
describe the experimental elliptic flow $v_2$ and the triangular flow $v_3$
simultaneously in ultra-central collisions. The problem, known as the
"ultra-central flow puzzle", is specifically that hydrodynamics-based models
predict the flow ratio of the two-particle cumulant method $v_2\{2\}/v_3\{2\} >
1$ while $v_2\{2\}/v_3\{2\} \sim 1$ in the experimental data. In this Letter,
we focus on the effects of hydrodynamic fluctuations during the space-time
evolution of the QGP fluid on the flow observables in the ultra-central
collisions. Using the (3+1)-dimensional integrated dynamical model which
includes relativistic fluctuating hydrodynamics, we analyze the anisotropic
flow coefficients $v_n\{2\}$ in 0-0.2% central Pb+Pb collisions at
$\sqrt{s_\text{NN}}=2.76~\text{TeV}$. We find that the hydrodynamic
fluctuations decrease the model overestimate of $v_2\{2\}/v_3\{2\}$ from the
experimental data by about 19% within the present setup of $\eta/s = 1/2\pi$.
This means that the hydrodynamic fluctuations qualitatively have an effect to
improve the situation for the puzzle, but the effect of the hydrodynamic
fluctuations alone is quantitatively insufficient to resolve the puzzle. The
decrease of the ratio largely depends on the shear viscosity $\eta/s$, which
calls for future comprehensive analyses with, for example, a realistic
temperature-dependent viscosity.
