Bonamy, D.; Chavanis, P.-H.; Cortet, P.-P.; Daviaud, F.; Dubrulle, B.; Renouf, M. Euler-like modelling of dense granular flows: application to a rotating drum. (English) Zbl 1188.76266 Eur. Phys. J. B, Condens. Matter Complex Syst. 68, No. 4, 619-627 (2009). Summary: General conservation equations are derived for 2D dense granular flows from the Euler equation within the Boussinesq approximation. In steady flows, the 2D fields of granular temperature, vorticity and stream function are shown to be encoded in two scalar functions only. We checked such prediction on steady surface flows in a rotating drum simulated through the Non-Smooth Contact Dynamics method even though granular flows are dissipative and therefore not necessarily compatible with Euler equation. Finally, we briefly discuss some possible ways to predict theoretically these two functions using statistical mechanics. Cited in 2 Documents MSC: 76T25 Granular flows PDFBibTeX XMLCite \textit{D. Bonamy} et al., Eur. Phys. J. B, Condens. Matter Complex Syst. 68, No. 4, 619--627 (2009; Zbl 1188.76266) Full Text: DOI arXiv References: [1] H.M. Jaeger, S.R. Nagel, R.P. Behringer, Rev. Mod. Phys. 68, 1259 (1996) [2] S.B. Savage, D.J. Jeffrey, J. Fluid Mech. 110, 255 (1981) [3] J.T. Jenkins, S.B. Savage, J. Fluid Mech. 130, 187 (1983) [4] C.K.K. Lun, S.B. Savage, Acta Mech. 63, 15 (1986) [5] R.M. Nedderman, Statics and Kinematics of Granular Materials (Cambridge University Press, Cambridge, 1992) [6] G.D.R. Midi, Eur. Phys. J. E 14, 341 (2004) [7] P. Mills, D. Loggia, M. Texier, Europhys. Lett. 45, 733 (1999) [8] B. Andreotti, S. Douady, Phys. Rev. E 63, 031305 (2001) [9] J.T. Jenkins, D.M. Hanes, Phys. Fluids 14, 1228 (2002) [10] D. Bonamy, P. Mills, Europhys. Lett. 63, 42 (2003) [11] J. Rajchenbach, Phys. Rev. Lett 90, 144302 (2003) [12] S.B. Savage, J. Fluid Mech. 377, 1 (1998) [13] L. Bocquet, W. Losert, D. Schalk, T.C. Lubensky, J.P. Gollub, Phys. Rev. E 65, 01307 (2002) [14] L.S. Mohan, K.K. Rao, P.R. Nott, J. Fluid Mech. 457, 377 (2002) [15] I.S. Aranson, L.S. Tsimring, Phys. Rev. E 65 061303 (2002) [16] O. Pouliquen, R. Gutfraind, Phys. Rev. E 53, 552 (1996) [17] G. Debregeas, C. Josserand, Europhys. Lett. 52, 137 (2000) [18] O. Pouliquen, Y. Forterre, S.L. Dizes, Adv. Complex System 4, 441 (2001) [19] A. Lemaitre, Phys. Rev. Lett. 89, 064303 (2002) [20] I. Iordanoff, M.M. Khonsari, ASME J. Tribol. 14, 341 (2004) [21] F. Da Cruz, S. Eman, M. Prochnow, J.-N. Roux, F. Chevoir, Phys. Rev. E 72, 021309 (2005) [22] P. Jop, Y. Forterre, O. Pouliquen, Nature 441, 727 (2006) [23] N. Leprovost, B. Dubrulle, P.-H. Chavanis, Phys. Rev. E 71, 036311 (2005) [24] N. Leprovost, B. Dubrulle, P.-H. Chavanis, Phys. Rev. E 73, 046308 (2006) [25] R. Monchaux, F. Ravelet, B. Dubrulle, A. Chiffaudel, F. Daviaud, Phys. Rev. Lett. 96, 124502 (2006) [26] R. Monchaux, P.-P. Cortet, P.-H. Chavanis, A. Chiffaudel, F. Daviaud, P. Diribarne, B. Dubrulle, Phys. Rev. Lett. 101, 174502 (2008) [27] M. Renouf, D. Bonamy, F. Dubois, P. Alart, Phys. Fluids 17, 103303 (2005) [28] J. Rajchenbach, Adv. Phys. 49, 229 (2000) [29] D. Bonamy, F. Daviaud, L. Laurent, Phys. Fluids 14, 1666 (2002) [30] D. Bonamy, F. Daviaud, L. Laurent, P. Mills, Gran. Matt. 4, 183 (2003) [31] P. Jop, Y. Forterre, O. Pouliquen, J. Fluid Mech. 541, 167 (1990) [32] R.J. Speedy, J. Chem. Phys. 110, 4559 (1999) [33] P.-H. Chavanis, J. Sommeria, Phys Rev. Lett. 78, 3302 (1997) [34] P.-H. Chavanis, J. Sommeria, Phys Rev. E 65, 026302 (2002) [35] J.-J. Moreau, in Non Smooth Mechanics and Applications, CISM Courses and Lectures, edited by P.-D. Panagiotopoulos (Springer-Verlag, Wien, New York, 1988), p. 1 [36] M. Jean, Comp. Meth. Appl. Mech. Engrg. 177, 235 (1999) [37] M. Renouf, P. Alart, Comp. Meth. Appl. Mech. Engrg. 194, 2019 (2004) [38] M. Renouf, F. Dubois, P. Alart, J. Comput. Appl. Math. 168, 375 (2004) [39] D. Bonamy, F. Daviaud, L. Laurent, M. Bonetti, J.-P. Bouchaud, Phys. Rev. Lett. 89, 034301 (2002) [40] O. Reynolds, Phyl. Mag. Ser. 5 20, 469 (1885) [41] T.S. Komatsu, S. Inagasaki, N. Nakagawa, S. Nasuno, Phys. Rev. Lett. 86, 1757 (2001) [42] S. Courrech du Pont, R. Fisher, P. Gondret, B. Perrin, M. Rabaud, Phys. Rev. Lett. 94, 048003 (2005) [43] J. Crassous, J.-F. Metayer, P. Richard, C. Laroche, J. Stat. Mech., P03009 (2008) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.