The $mathrm{n^{th}}$-order linear flow coefficients $mathrm{v^L_n , (n=2,3,4,5)}$, and the corresponding nonlinear mode-coupled ($mathrm{mc}$) coefficients $mathrm{v^{mc}_{4,(2,2)}}$, $mathrm{v^{mc}_{5,(2,3)}}$, $mathrm{v^{mc}_{6,(3,3)}}$ and $mathrm{v^{mc}_{6,(2,2,2)}}$, are studied for Pb+Pb collisions at $sqrt{s_{_{rm NN}}} = 2.76$ TeV. Both sets of coefficients indicate a common acoustic scaling pattern of exponential viscous modulation, with a rate proportional to the square of the harmonic numbers and the mean transverse momenta (respectively), and inversely proportional to the cube root of the charged particle multiplicity ($mathrm{(N_{ch})^{1/3}}$), that characterizes the dimensionless size of the systems produced in the collisions. These patterns and their associated scaling parameters, provide new stringent constraints for eccentricity independent estimates of the specific shear viscosity ($eta/s$) and the viscous correction to the thermal distribution function for the matter produced in the collisions. They also give crucial constraints for extraction of the initial-state eccentricity spectrum.
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