Meandering instability of air flow in a granular bed: self-similarity and fluid-solid duality

TL;DR

This study investigates the meandering instability of air flow in a granular bed through experiments and theory, revealing self-similar shapes and a fluid-solid duality that could inform multiple scientific disciplines.

Contribution

It introduces a universal phase diagram for flow regimes in granular beds and develops a theoretical model explaining the physics behind air flow meandering.

Findings

Flow regimes depend on flow rate and bed thickness when properly normalized.

Meandering shapes exhibit self-similarity similar to rivers.

Theoretical analysis based on force balance and instability explains experimental results.

Abstract

Meandering instability is familiar to everyone through river meandering or small rivulets of rain flowing down a windshield. However, its physical understanding is still premature, although it could inspire researchers in various fields, such as nonlinear science, fluid mechanics and geophysics, to resolve their long-standing problems. Here, we perform a small-scale experiment in which air flow is created in a thin granular bed to successfully find a meandering regime, together with other remarkable fluidized regimes, such as a turbulent regime. We discover that phase diagrams of the flow regimes for different types of grains can be universally presented as functions of the flow rate and the granular-bed thickness when the two quantities are properly renormalized. We further reveal that the meandering shapes are self-similar as was shown for meandering rivers. The experimental findings are explained by theory, with elucidating the physics. The theory is based on force balance, a minimum-dissipation principle, and a linear-instability analysis of a continuum equation that takes into account the fluid-solid duality, i.e., the existence of fluidized and solidified regions of grains along the meandering path. The present results provide fruitful links to related issues in various fields, including fluidized bed reactors in industry.