  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.

Soft Condensed Matter;Statistical Mechanics;Pattern Formation and Solitons;Fluid Dynamics;Geophysics