“…Although there are other models that consider the problem of avalanche motion over curved slopes ͑e.g., Gray et al, 3 Denlinger and Iverson, 4,5 Kerswell, 6 Ancey, 7 Pitman et al, 8,9 Maeno and Nishimura, 26 Norem et al, 27,28 Savage and Nohguchi, 29 Savage and Hutter, 30 Iverson et al, 31 see also the Same report edited by Harbitz, 32 Bouchut and Westdickenberg, 33 and Tai and Kuo 34 ͒, the model equations considered in this paper are the first to explicitly include curvature and torsion effects in a systematic manner ͑see Pudasaini et al͒. 16,17,35 This makes the extended model amenable to realistic granular flow motions down arbitrary guiding topographies or transportation of granular masses in general channels in industrial process engineering.…”