Velocity Correlations in Dense Granular Flows

Velocity fluctuations of grains flowing down a rough inclined plane are experimentally studied. The grains at the free surface exhibit fluctuating motions, which are correlated over a few grain diameters. The characteristic correlation length is shown to depend on the inclination of the plane and not on the thickness of the flowing layer. This result strongly supports the idea that dense granular flows are controlled by a characteristic length larger than the particle diameter.

Figure 1

Flow threshold: (●) experimental measurements of the deposit $h_{\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{p}}(\theta )$. Inset: sketch of the experimental setup.

Figure 2

Fluctuating velocity of particles at the free surface (a) $\theta =21°$, $h/d=13.7$ and (b) $\theta =26°$, $h/d=9.3$.

Figure 3

Mean velocity fluctuations $\delta V/\sqrt{gd}$ as a function of the mean shear rate $U_{s}d/h\sqrt{gd}$ for different inclinations $\theta$. Inset: log-log plot.

Figure 4

The four normalized correlation functions for $\theta =20°$ and $h/d=19.8$: $C_{xx}$ (▲), $C_{yy}$ (○), $C_{yx}$ (▼), and $C_{xy}$ (□).

Figure 5

Normalized correlation function $C_{xx}$ for different flow thicknesses at three inclinations.

Figure 6

Mean normalized correlation function for different $\theta$.

Figure 7

The four correlation lengths $L_{xx}$ (▲), $L_{yy}$ (○), $L_{yx}$ (▼), and $L_{xy}$ (□), as functions of $\theta$. Inset: $L_{xx}$ as a function of $h_{\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{p}}$. The error bars give the measurement dispersion when the correlation lengths are computed from individual runs and not from the mean correlation functions of Fig. 6.