Power Spectra of Velocity Fluctuations in Granular Heap Flow

This Letter used speckle visibility spectroscopy to probe velocity fluctuations in three-dimensional granular heap flow. The mean velocity profile comprises a fast-flowing surface layer over a creeping layer. In both layers, velocity fluctuations are scale invariant and self-similar, and the velocity spectra demonstrate power-law scaling, E(f)∝f^{α}. In the surface layer, α is between -1.0 and -0.8, consistent with Hwa and Kardar's "running" sandpile model, indicative of a dynamically self-organized critical state. In the creep layer, α decreases with depth, reaching ≈-1.5 at a sufficiently deep layer; its theoretical basis remains unclear. Analysis of the fluctuation velocity distributions provides further insight into the microscopic origins of the spectrum. These findings may help resolve the long-standing puzzle of flow localization in gravity-driven granular flows, despite a uniform shear stress-to-pressure ratio.