@article{5897e2d235c84bceab07ab39e714a700,
title = "Theoretical and numerical structure for unstable two-dimensional detonations",
abstract = "The first detailed comparison between predictions of theories for detonatios are presented here. Provided the unperturbed Z-N-D profile only exhibits instability at long transverse wavelengths with a simple stability diagram, the computed regular cell spacing is found to agree remarkably well with simple theories based on the most unstable linearized wavelengths when the channel width is not too large. Neither the geometric acoustic theories nor theories based upon a linearized unstable wavelength provide an accurate prediction of the computed cell-spacing for Z-N-D profiles with a complex stability diagram such as those that are unstable at short transverse wavelengths. Several new features of detonation instability are also documented here through the numerical simulations, including regimes exhibiting the transition to fully developed turbulence in the wake of the unstable detonation front as the activation energy and heat release are increased. Furthermore, the computations indicate that this strong turbulence contributes to the irregularity of the cellular pattern.",
author = "Anne Bourlioux and Majda, {Andrew J.}",
note = "Funding Information: complexitoyftwo-dimensiontaulrbulenceis 10. Majda, A., and Roytburd,V.,Stud. Appl. Math. (in observed. press). 11. Strehlow,R . A., and FernandesF,. D., Combust. Flame 9:31-58( 1965). 12. Boris, J. P. and OranE, . S., NumericaSl imulationof {"} ReaeticFel ow, ElsevierN, ew York, 1987,p p. 518 549. 13. Guirguis,R ., Oran, E. S., and KailasanathK,. , Corn-bust. Flame 65:339-36(51 986). 14. KailasanathK,. , Oran, E. S., Boris, J. P., and Young, T. R., CombustF. lame6 1:199-20(91 985). 15. Oran, E. S., Young, T. R., Boris, J. P., Piconc,J . M., and Edwards,D . H., NineteentShy mposium(In terna-tional) on CombustionT,h e CombustioInn stitute, Pittsburgh1, 982,p p. 573-582. 16. Taki, S., and FumiwaraT, ., A/AA J. 16:73(1 973). 17. Taki, S., and Fumiwara,T ., EighteenthS ymposium (Internationalo) n CombustioTnh, e CombustioInns ti-tute, Pittsburg1h9, 81p, p. 1641 1649. 18. Bourlioux,A ., and Majda, A., AIAA Progress Series with Proceedingosf 13th ICDERS Meeting, Nagoya, Japan, 1991( in press). 19. BourliouxA, ., Majda, A., and RoytburdV, ., SIAMJ. Appl. Math. 51:303-34(31 991). 20. Bourlioux, A., Ph.D. thesis, Princeton University, 1991. 21. BourliouxA, ., Majda,A ., and RoytburdV, ., l)ynamic Issues in Combustion( P. Fife, A. Linan, and F. Williams, Eds.), IMA Volumesi n Mathematics and its Applications1, 991,V ol. 35, pp. 63-83. Then umericacla lculations in this article where 22. Colella, P. and Woodward,P ., J. Comput. Phys. performeodn the CRAY-YMP at theN SF Pitts-54:174-20(11 984). burgh SupeCro mputeIrn stituteA. nneBourlioux (1989). Berger,M ., and Colella,P ., J. is{"} a fellowo f the Miller Research InstitAunte-. 24. Chern, I., and Colella, P., Preprint UCRL-97200, drewJ . Majda was partially supported by grants LawrenceL ivermoreN ationalL aboratory(1 987). ARO DAALO3-89-K-O013O, NR NOOO14-89-J-25. ErpenbeckJ,. J., Phys. Fluids1' 3:2007-202(619 70). 1044.P0000a3n, dNSF DMS-9001805. 26. ErpenbeckJ,. J., TwelfthS ymposiumon Combustion, The Combustion Institute, Pittsburgh, 1969, pp. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.",
year = "1992",
month = sep,
doi = "10.1016/0010-2180(92)90084-3",
language = "English (US)",
volume = "90",
pages = "211--229",
journal = "Combustion and Flame",
issn = "0010-2180",
publisher = "Elsevier Inc.",
number = "3-4",
}