Acoustic Rayleigh Wave Turbulence in Soft Viscoelastic Matter

Evidence of discrete acoustic Rayleigh wave turbulence (DARWT) is reported on the free surface of complex viscoelastic materials under monochromatic excitation. These surface elastic non-linear Rayleigh waves exhibit dispersionless dynamics governed by bulk shear rigidity at coexistence with dispersive capillary waves supported by surface tension. Using Laser Doppler Vibrometry (LDV), the discrete Kolmogorov-Zakharov (KZ) spectrum is measured, characterized by a power-law envelope in an inertial cascade of discrete harmonics. When shear rigidity dominates, KZ-spectrum characterized by an ω^-5/2 acoustic fingerprint is observed as a conservative solid-like scaling, theoretically predicted from the exact three-wave dispersionless resonance. Conversely, when surface tension dominates over bulk stresses, dispersive CW behavior under the usual ω^-17/6 liquid-like scaling is recovered. These findings support a unique theoretical framework for understanding conservative DARWT and advance the field of surface wave turbulence in viscoelastic media with markedly non-Newtonian rheology. Acoustic Rayleigh wave turbulence represents a conservative mechanism for dispersionless energy transport through weakly nonlinear wave interactions across scales, with relevance to various physics fields, from soft matter and biological systems up to geophysical flows.