arXiv preview of Proximity to Jamming Governs Acoustic Attenuation in Damped Packings

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The Problem

When an acoustic wave propagates through a fluid-saturated granular packing (e.g., water-filled sand or gravel), the wave amplitude decays over distance — this is attenuation. A well-established empirical observation is that at a certain point, the spatial attenuation rate changes from a quadratic scaling to a linear scaling with frequency. Despite decades of experimental data, no framework grounded in grain-scale physics had explained this dependence.

Our Approach

My collaborators and I performed particle-based numerical simulations in which every grain in a disordered, jammed packing is resolved individually, with the interstitial fluid accounted for. We computed the damped vibrational (harmonic) modes of the packing and also propagated explicit wavefronts through it, varying three control parameters:

• the frequency of the excitation or wave,
• the confining pressure, and
• the grain-contact dissipation (energy lost per grain–grain contact event).

Key Findings

At a pressure-dependent critical frequency, both the eigenmodes and the propagating waves undergo a sharp transition:

• Below the critical frequency: The grains move in a coherent, continuum-like fashion. The spatial attenuation rate scales quadratically with frequency and linearly with contact dissipation, consistent with classical viscous-fluid behavior.
• Above the critical frequency: The motion becomes incoherent and localized at the particle scale, with energy redistributed through scattering between grains. Here, attenuation scales linearly with frequency and sublinearly with contact dissipation — the regime that had avoided explanation.

The spatial structure of the damped eigenmodes and the measured wave propagation characteristics agree with one another at the same critical frequency, and both are consistent with a large body of experimental data that no prior grain-scale model could reproduce.

What We Propose

We call this mechanism Jammed-Network Scattering (JNS) and put forward it as a grain-scale framework for the acoustics of fluid-saturated granular media. In essence, the observed linear frequency dependence of attenuation is not a material property of the fluid but an emergent consequence of the system crossing from coherent, collective motion into incoherent, particle-scale scattering as the wavelength becomes comparable to the grain spacing.