Unified Flow Rule of Undeveloped and Fully Developed Dense Granular Flows Down Rough Inclines
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912193359904768 |
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| author | Wu, Yanbin Pähtz, Thomas Guo, Zixiao Jing, Lu Duan, Zhao He, Zhiguo |
| author_facet | Wu, Yanbin Pähtz, Thomas Guo, Zixiao Jing, Lu Duan, Zhao He, Zhiguo |
| contents | We report on chute measurements of the free-surface velocity $v$ in dense flows of spheres and diverse sands and spheres-sand mixtures down rough inclines. These and previous measurements are inconsistent with standard flow rules, in which the Froude number $v/\sqrt{gh}$ scales linearly with $h/h_s$ or $(\tanθ/μ_r)^2h/h_s$, where $μ_r$ is the dynamic friction coefficient, $h$ the flow thickness, and $h_s(θ)$ its smallest value that permits a steady, uniform dense flow state at a given inclination angle $θ$. This is because the characteristic length $L$ a flow needs to fully develop can exceed the chute or travel length $l$ and because neither rule is universal for fully developed flows across granular materials. We use a dimensional analysis motivated by a recent unification of sediment transport to derive a flow rule that solves both problems in accordance with our and previous measurements: $v=v_\infty[1-\exp(-l/L)]^{1/2}$, with $v_\infty\proptoμ_r^{3/2}\left[(\tanθ-μ_r)h\right]^{4/3}$ and $L\proptoμ_r^3\left[(\tanθ-μ_r)h\right]^{5/3}h$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10631 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unified Flow Rule of Undeveloped and Fully Developed Dense Granular Flows Down Rough Inclines Wu, Yanbin Pähtz, Thomas Guo, Zixiao Jing, Lu Duan, Zhao He, Zhiguo Soft Condensed Matter Fluid Dynamics Geophysics We report on chute measurements of the free-surface velocity $v$ in dense flows of spheres and diverse sands and spheres-sand mixtures down rough inclines. These and previous measurements are inconsistent with standard flow rules, in which the Froude number $v/\sqrt{gh}$ scales linearly with $h/h_s$ or $(\tanθ/μ_r)^2h/h_s$, where $μ_r$ is the dynamic friction coefficient, $h$ the flow thickness, and $h_s(θ)$ its smallest value that permits a steady, uniform dense flow state at a given inclination angle $θ$. This is because the characteristic length $L$ a flow needs to fully develop can exceed the chute or travel length $l$ and because neither rule is universal for fully developed flows across granular materials. We use a dimensional analysis motivated by a recent unification of sediment transport to derive a flow rule that solves both problems in accordance with our and previous measurements: $v=v_\infty[1-\exp(-l/L)]^{1/2}$, with $v_\infty\proptoμ_r^{3/2}\left[(\tanθ-μ_r)h\right]^{4/3}$ and $L\proptoμ_r^3\left[(\tanθ-μ_r)h\right]^{5/3}h$. |
| title | Unified Flow Rule of Undeveloped and Fully Developed Dense Granular Flows Down Rough Inclines |
| topic | Soft Condensed Matter Fluid Dynamics Geophysics |
| url | https://arxiv.org/abs/2501.10631 |