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

Meanderinginstability is familiar to everyone through river meanderingor 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 mechanicsand 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 meanderingregime, 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 meanderingshapes are self-similar as was shown for meanderingrivers. 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 meanderingpath. The present results provide fruitful links to related issues in various fields, including fluidized bed reactors in industry.