Journal
PHYSICS OF FLUIDS
Volume 26, Issue 12, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.4904520
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Funding
- School of Mathematics of the University of Manchester [EPSRC EP/I01912X/1]
- European Union (European Social Fund)
- Greek national funds through the Operational Program Education and Lifelong Learning of the National Strategic Reference Framework-Research Funding Program THALES: Investing in knowledge society through the European Social Fund [MIS 380238]
- NERC [NE/E003206/1, NE/G523747/11]
- EPSRC [EP/I019189/1, EP/K00428X/1]
- EPSRC DTA
- Margaret Elizabeth Lee Fellowship
- EPSRC [EP/I019189/1, EP/I01912X/1, EP/K00428X/1] Funding Source: UKRI
- NERC [NE/K003011/1, NE/E003206/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/K00428X/1, EP/I01912X/1, EP/I019189/1] Funding Source: researchfish
- Natural Environment Research Council [NE/K003011/1, NE/E003206/1] Funding Source: researchfish
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We study a system in which granular matter, flowing down an inclined chute with periodic boundary conditions, organizes itself in a train of roll waves of varying size. Since large waves travel faster than small ones, the waves merge, and their number gradually diminishes. This coarsening process, however, does not generally proceed to the ultimate one-wave state: Numerical simulations of the dynamical equations (being the granular analogue of the shallow water equations) reveal that the process is arrested at some intermediate stage. This is confirmed by a theoretical analysis, in which we show that the roll waves cannot grow beyond a certain limiting size (which is fully determined by the system parameters), meaning that on long chutes the material necessarily remains distributed over more waves. We determine the average lifetime tau(N) of the successive N-wave states, from the initial state with typically N = 50 waves (depending on the length of the periodic domain) down to the final state consisting of only a handful of waves (N = N-arr). At the latter value of N, the lifetime tau(N) goes to infinity. At this point the roll waves all have become equal in size and are traveling with the same speed. Our theoretical predictions for the successive lifetimes tau(N) and the value for N-arr show good agreement with the numerical observations. (C) 2014 AIP Publishing LLC.
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