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- W4306989166 abstract "This paper describes, from a theoretical point of view, the appearance and characteristics of granular roll waves in chute flow, and the maximal size these waves can attain for a given influx of material into the system. Granular roll waves are steady travelling wave solutions of the generalized Saint-Venant equations for flowing granular matter, appearing when the Froude number $Fr$ of the incoming flow exceeds a critical value, $Fr>Fr_{cr}$ . We focus upon the phase space of the corresponding dynamical system, where the roll waves take the form of a stable limit cycle around an unstable fixed point; this limit cycle gives precise information on the size and periodicity of the roll wave. It is found that, for any given value of $Fr$ , the limit cycle cannot become arbitrarily large because it is constrained by a homoclinic loop in phase space. Roll waves of larger amplitude can be generated by increasing the Froude number $Fr$ ." @default.
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- W4306989166 date "2022-10-21" @default.
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- W4306989166 title "On the shape and size of granular roll waves" @default.
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- W4306989166 doi "https://doi.org/10.1017/jfm.2022.811" @default.
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