Velocity Correlations in Dense Gravity Driven Granular Chute Flow

TL;DR

This study numerically investigates velocity correlations in dense, gravity-driven granular flow down an inclined plane, revealing exponential decay of correlations and their dependence on various system parameters, with implications for understanding granular rheology.

Contribution

It provides new insights into the structure and scale of velocity correlations in dense granular flows, highlighting their dependence on system parameters and challenging existing theoretical expectations.

Findings

Correlation lengths are typically small, about a particle diameter.

Correlation lengths increase logarithmically with the minimum pile height for flow.

Velocity correlations decay exponentially with separation distance.

Abstract

We report numerical results for velocity correlations in dense, gravity-driven granular flow down an inclined plane. For the grains on the surface layer, our results are consistent with experimental measurements reported by Pouliquen. We show that the correlation structure within planes parallel to the surface persists in the bulk. The two-point velocity correlation function exhibits exponential decay for small to intermediate values of the separation between spheres. The correlation lengths identified by exponential fits to the data show nontrivial dependence on the averaging time $\dt$ used to determine grain velocities. We discuss the correlation length dependence on averaging time, incline angle, pile height, depth of the layer, system size and grain stiffness, and relate the results to other length scales associated with the rheology of the system. We find that correlation lengths are typically quite small, of the order of a particle diameter, and increase approximately logarithmically with a minimum pile height for which flow is possible, $\hstop$, contrary to the theoretical expectation of a proportional relationship between the two length scales.