Papers

Zuccoli, E., Brambley, E.J. and Barkley, D. (2025) ‘Deep-water closure model for surface waves on axisymmetric swirling flowsLink opens in a new window’, Physical Review Fluids, 10(2), p. 024801. doi.org/10.1103/PhysRevFluids.10.024801Link opens in a new window
Benavides, S.J. and Barkley, D. `Model for transitional turbulence in a planar shear flowLink opens in a new window', (in review).
Zuccoli, E., Brambley, E.J. and Barkley, D. (2024) ‘Trapped free surface waves for a Lamb–Oseen vortex flowLink opens in a new window’, Journal of Fluid Mechanics, 997, p. A40. doi:10.1017/jfm.2024.645Link opens in a new window.
Gomé, S., Riviere, A., Tuckerman, L.S. and Barkley, D. (2024) ‘Phase transition to turbulence via moving frontsLink opens in a new window’, Physical Review Letters, 132, p. 264002. doi:10.1103/PhysRevLett.132.264002Link opens in a new window.
Gomé, S., Tuckerman, L.S. and Barkley, D. (2023) ‘Patterns in transitional shear turbulence. Part 1. Energy transfer and mean-flow interactionLink opens in a new window’, Journal of Fluid Mechanics, 964, p. A16. doi:10.1017/jfm.2023.288Link opens in a new window.
Gomé, S., Tuckerman, L.S. and Barkley, D. (2023) ‘Patterns in transitional shear turbulence. Part 2. Emergence and optimal wavelengthLink opens in a new window’, Journal of Fluid Mechanics, 964, p. A17. doi:10.1017/jfm.2023.289Link opens in a new window.
Avila, M., Barkley, D. and Hof, B. (2023) ‘Transition to Turbulence in Pipe Flow’, Annual Review of Fluid Mechanics, 55, pp. 575–602. doi:10.1146/annurev-fluid-120720-025957Link opens in a new window.
Gomé, S., Tuckerman, L.S. and Barkley, D. (2022) ‘Extreme events in transitional turbulenceLink opens in a new window’, Philosophical Transactions of the Royal Society A, 380(2212), p. 20210036. doi:10.1098/rsta.2021.0036Link opens in a new window.
Barkley, D. (2020) ‘A fluid mechanic’s analysis of the teacup singularityLink opens in a new window’, Proceedings of the Royal Society A, 476(2243), p. 20200348. doi:10.1098/rspa.2020.0348Link opens in a new window.
Gomé, S., Tuckerman, L.S. and Barkley, D. (2020) ‘Statistical transition to turbulence in plane channel flowLink opens in a new window’, Physical Review Fluids, 5(8), p. 083905. doi:10.1103/PhysRevFluids.5.083905Link opens in a new window.
Tuckerman, L.S., Chantry, M. and Barkley, D. (2020) ‘Patterns in Wall-Bounded Shear Flows’, Annual Review of Fluid Mechanics, 52, pp. 343–367. doi:10.1146/annurev-fluid-010719-060221Link opens in a new window.
Barkley, D. (2019) ‘Taming turbulent fronts by bending pipes’, Journal of Fluid Mechanics, 872, pp. 1–4. doi:10.1017/jfm.2019.340Link opens in a new window.
Dessup, T., Tuckerman, L.S., Wesfreid, J.E., Barkley, D. and Willis, A.P. (2018) ‘Self-sustaining process in Taylor-Couette flowLink opens in a new window’, Physical Review Fluids, 3(12), p. 123902. doi:10.1103/PhysRevFluids.3.123902Link opens in a new window.
Langham, J., Bense, H. and Barkley, D. (2018) ‘Modeling shape selection of buckled dielectric elastomersLink opens in a new window’, Journal of Applied Physics, 123(6), p. 065102. doi:10.1063/1.5012848Link opens in a new window.
Chantry, M., Tuckerman, L.S. and Barkley, D. (2017) ‘Universal continuous transition to turbulence in a planar shear flowLink opens in a new window’, Journal of Fluid Mechanics, 824, R1. doi:10.1017/jfm.2017.405Link opens in a new window.
Song, B., Barkley, D., Hof, B. and Avila, M. (2017) ‘Speed and structure of turbulent fronts in pipe flowLink opens in a new window’, Journal of Fluid Mechanics, 813, pp. 1045–1059. doi:10.1017/jfm.2017.14Link opens in a new window.
Barkley, D. (2016) ‘Theoretical perspective on the route to turbulence in a pipeLink opens in a new window’, Journal of Fluid Mechanics, 803, P1. doi:10.1017/jfm.2016.465Link opens in a new window.
Chantry, M., Tuckerman, L.S. and Barkley, D. (2016) ‘Turbulent-laminar patterns in shear flows without wallsLink opens in a new window’, Journal of Fluid Mechanics, 791, R8. doi:10.1017/jfm.2016.92Link opens in a new window.
Barkley, D., Song, B., Mukund, V., Lemoult, G., Avila, M. and Hof, B. (2015) ‘The rise of fully turbulent flowLink opens in a new window’, Nature, 526, pp. 550–553. doi:10.1038/nature15701Link opens in a new window.
Turton, S.E., Tuckerman, L.S. and Barkley, D. (2015) ‘Prediction of frequencies in thermosolutal convection from mean flowsLink opens in a new window’, Physical Review E, 91(4), p. 043009. doi:10.1103/PhysRevE.91.043009Link opens in a new window.
Langham, J., Biktasheva, I.V. and Barkley, D. (2014) ‘Asymptotic dynamics of reflecting spiral wavesLink opens in a new window’, Physical Review E, 90(6), p. 062902. doi:10.1103/PhysRevE.90.062902Link opens in a new window.
Langham, J. and Barkley, D. (2013) ‘Non-specular reflections in a macroscopic system with wave-particle duality: Spiral waves in bounded mediaLink opens in a new window’, Chaos, 23(1), p. 013134. doi:10.1063/1.4793783Link opens in a new window.
Barkley, D. (2012) ‘Pipe flow as an excitable mediumLink opens in a new window’, Revista Cubana de Física, 29(1E), p. 27.
Barkley, D. (2011) ‘Modeling the transition to turbulence in shear flowsLink opens in a new window’, Journal of Physics: Conference Series, 318, p. 032001.
Barkley, D. (2011) ‘Simplifying the complexity of pipe flowLink opens in a new window’, Physical Review E, 84(1), p. 016309. doi:10.1103/PhysRevE.84.016309Link opens in a new window.
Avila, K., Moxey, D., de Lozar, A., Avila, M., Barkley, D. and Hof, B. (2011) ‘The onset of turbulence in pipe flowLink opens in a new window’, Science, 333(6039), pp. 192–196. doi:10.1126/science.1203223Link opens in a new window.
Tuckerman, L.S. and Barkley, D. (2011) ‘Patterns and dynamics in transitional plane Couette flowLink opens in a new window’, Physics of Fluids, 23(4), p. 041301. doi:10.1063/1.3580263Link opens in a new window.
Marais, C., Godoy-Diana, R., Barkley, D. and Wesfreid, J.E. (2011) ‘Convective instability in inhomogeneous media: Impulse response in the subcritical cylinder wakeLink opens in a new window’, Physics of Fluids, 23(1), p. 014104. doi.org/10.1063/1.3531724Link opens in a new window.
Cantwell, C.D. and Barkley, D. (2010) ‘Computational study of subcritical response in flow past a circular cylinderLink opens in a new window’, Physical Review E, 82(2), p. 026315. doi:10.1103/PhysRevE.82.026315Link opens in a new window.
Biktasheva, I.V., Barkley, D., Biktashev, V.N. and Foulkes, A.J. (2010) ‘Computation of the drift velocity of spiral waves using response functionsLink opens in a new window’, Physical Review E, 81(6), p. 066202. doi:10.1103/PhysRevE.81.066202Link opens in a new window.
Moxey, D. and Barkley, D. (2010) ‘Distinct large-scale turbulent-laminar states in transitional pipe flowLink opens in a new window’, Proceedings of the National Academy of Sciences, 107(18), pp. 8091–8096. doi.org/10.1073/pnas.0909560107Link opens in a new window.
Bordja, L., Tuckerman, L.S., Martin Witkowski, L., Navarro, M.C., Barkley, D. and Bessiah, R. (2010) ‘Influence of counter-rotating von Karman flow on cylindrical Rayleigh-Bénard convectionLink opens in a new window’, Physical Review E, 81(3), p. 036322. doi:10.1103/PhysRevE.81.036322Link opens in a new window.
Cantwell, C.D., Barkley, D. and Blackburn, H.M. (2010) ‘Transient growth analysis of flow through a sudden expansion in a circular pipeLink opens in a new window’, Physics of Fluids, 22(3), p. 034101. doi:10.1063/1.3313931Link opens in a new window.
Biktashev, V.N., Barkley, D. and Biktasheva, I.V. (2010) ‘Orbital motion of spiral waves in excitable mediaLink opens in a new window’, Physical Review Letters, 104(5), p. 058302. doi:10.1103/PhysRevLett.104.058302Link opens in a new window.
Biktasheva, I.V., Barkley, D., Biktashev, V.N., Bordyugov, G.V. and Foulkes, A.J. (2009) ‘Computation of the response functions of spiral waves in active mediaLink opens in a new window’, Physical Review E, 79(5), p. 056702. doi:10.1103/PhysRevE.79.056702Link opens in a new window.
Blackburn, H.M., Sherwin, S.J. and Barkley, D. (2008) ‘Convective instability and transient growth in steady and pulsatile stenotic flowsLink opens in a new window’, Journal of Fluid Mechanics, 607, pp. 267–277. doi:10.1017/S0022112008001717Link opens in a new window.
Barkley, D., Blackburn, H.M. and Sherwin, S.J. (2008) ‘Direct optimal growth analysis for timesteppersLink opens in a new window’, International Journal for Numerical Methods in Fluids, 57(9), pp. 1435–1458. doi:10.1002/fld.1824Link opens in a new window.
Blackburn, H.M., Barkley, D. and Sherwin, S.J. (2008) ‘Convective instability and transient growth in flow over a backward-facing stepLink opens in a new window’, Journal of Fluid Mechanics, 603, pp. 271–304. doi:10.1017/S0022112008001109Link opens in a new window.
Barkley, D. (2008) ‘Barkley Model’, Scholarpedia - The Free Peer-Reviewed Encyclopedia, 3(11), p. 1877. Available at: http://www.scholarpedia.org/article/Barkley_modelLink opens in a new window.
Barkley, D. and Tuckerman, L.S. (2007) ‘Mean flow of turbulent-laminar patterns in plane Couette flowLink opens in a new window’, Journal of Fluid Mechanics, 576, pp. 109–137. doi:10.1017/S002211200600454XLink opens in a new window.
Barkley, D. (2006) ‘Linear analysis of the cylinder wake mean flowLink opens in a new window’, Europhysics Letters, 75(5), pp. 750–756. doi:10.1209/epl/i2006-10168-7Link opens in a new window.
Barkley, D., Kevrekidis, I.G. and Stuart, A.M. (2006) ‘The Moment Map: Nonlinear dynamics of density evolution via a few momentsLink opens in a new window’, SIAM Journal on Applied Dynamical Systems, 5(3), pp. 403–434. doi:10.1137/050638667Link opens in a new window.
Wheeler, P. and Barkley, D. (2006) ‘Computation of spiral spectraLink opens in a new window’, SIAM Journal on Applied Dynamical Systems, 5(1), pp. 157–177. doi:10.1137/050624273Link opens in a new window.
Barkley, D. and Tuckerman, L.S. (2005) ‘Computational study of turbulent-laminar patterns in Couette flowLink opens in a new window’, Physical Review Letters, 94(1), p. 014502. doi:10.1103/PhysRevLett.94.014502Link opens in a new window.
Barkley, D. (2005) ‘Confined three-dimensional stability analysis of the cylinder wakeLink opens in a new window’, Physical Review E, 71(1), p. 017301. doi:10.1103/PhysRevE.71.017301Link opens in a new window.
Barkley, D. and Tuckerman, L.S. (2005) ‘Turbulent-laminar patterns in plane Couette flowLink opens in a new window’, in IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions. Fluid Mechanics and Its Applications, 77, pp. 107–127. doi:10.1007/1-4020-4049-0_6Link opens in a new window.
Tuckerman, L.S. and Barkley, D. (2002) ‘Symmetry breaking and chaos in perturbed plane Couette flowLink opens in a new window’, Theoretical and Computational Fluid Dynamics, 16(2), pp. 91–97. doi:10.1007/s00162-002-0064-yLink opens in a new window.
Barkley, D., Gomes, M.G.M. and Henderson, R.D. (2002) ‘Three-dimensional instability in flow over a backward-facing stepLink opens in a new window’, Journal of Fluid Mechanics, 473, pp. 167–190. doi:10.1017/S002211200200232XLink opens in a new window.
Margerit, D. and Barkley, D. (2002) ‘Cookbook asymptotics for spiral and scroll waves in excitable mediaLink opens in a new window’, Chaos, 12(3), pp. 636–649. doi:10.1063/1.1494875Link opens in a new window.
Margerit, D. and Barkley, D. (2002) ‘Large-excitability asymptotics for scroll waves in three-dimensional excitable mediaLink opens in a new window’, Physical Review E, 66(3), p. 036214. doi:10.1103/PhysRevE.66.036214Link opens in a new window.
Margerit, D. and Barkley, D. (2001) ‘Selection of twisted scroll waves in three-dimensional excitable mediaLink opens in a new window’, Physical Review Letters, 86(1), pp. 175–178. doi:10.1103/PhysRevLett.86.175Link opens in a new window.
Mantel, R.M. and Barkley, D. (2001) ‘Parametric forcing of scroll-wave patterns in three-dimensional excitable mediaLink opens in a new window’, Physica D: Nonlinear Phenomena, 149(1–2), pp. 107–122. doi:10.1016/S0167-2789(00)00185-8Link opens in a new window.
Duckett, G. and Barkley, D. (2000) ‘Modeling the dynamics of cardiac action potentialsLink opens in a new window’, Physical Review Letters, 85(4), pp. 884–887. doi:10.1103/PhysRevLett.85.884Link opens in a new window.
Barkley, D., Tuckerman, L.S. and Golubitsky, M. (2000) ‘Bifurcation theory for three-dimensional flow in the wake of a circular cylinderLink opens in a new window’, Physical Review E, 61(5), pp. 5247–5252. doi:10.1103/PhysRevE.61.5247Link opens in a new window.
Tuckerman, L.S. and Barkley, D. (2000) ‘Bifurcation analysis for timesteppersLink opens in a new window’, in Doedel, E. and Tuckerman, L.S. (eds.) Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems. IMA Volumes in Mathematics and its Applications, vol. 119. New York: Springer, pp. 453–466. doi:10.1007/978-1-4612-1208-9_20Link opens in a new window.
Barkley, D. and Tuckerman, L.S. (1999) ‘Stability analysis of perturbed plane Couette flowLink opens in a new window’, Physics of Fluids, 11(5), pp. 1187–1195. doi:10.1063/1.869987Link opens in a new window.
Dowle, M., Mantel, R.M. and Barkley, D. (1997) ‘Fast simulations of waves in three-dimensional excitable mediaLink opens in a new window’, International Journal of Bifurcation and Chaos, 7(11), pp. 2529–2546. doi:10.1142/S0218127497001830Link opens in a new window.
Barkley, D. and Tuckerman, L.S. (1997) ‘Stokes preconditioning for the inverse power methodLink opens in a new window’, in Chattot, J.C. (ed.) 15th International Conference on Numerical Methods in Fluid Dynamics. Springer, New York. doi:10.1007/BFb0107081Link opens in a new window
Mantel, R.M. and Barkley, D. (1996) ‘Periodic forcing of spiral waves in excitable mediaLink opens in a new window’, Physical Review E, 54(5), pp. 4791–4802. doi:10.1103/PhysRevE.54.4791Link opens in a new window.
Barkley, D. and Henderson, R.D. (1996) ‘Floquet stability analysis of the periodic wake of a circular cylinderLink opens in a new window’, Journal of Fluid Mechanics, 322, pp. 215–241. doi:10.1017/S0022112096002777Link opens in a new window.
Henderson, R.D. and Barkley, D. (1996) ‘Secondary instability in the wake of a circular cylinderLink opens in a new window’, Physics of Fluids, 8(6), pp. 1683–1685. doi:10.1063/1.868939Link opens in a new window.
Barkley, D. (1995) ‘Spiral MeanderingLink opens in a new window’, in Kapral, R. and Showalter, K. (eds.) Chemical Waves and Patterns. Dordrecht: Springer, pp. 163–188. Available at: https://doi.org/10.1007/978-94-011-1156-0_5Link opens in a new window.
Schatz, M.F., Barkley, D. and Swinney, H.L. (1995) ‘Instabilities in spatially periodic channel flowLink opens in a new window’, Physics of Fluids, 7(2), pp. 344–358. doi:10.1063/1.868632Link opens in a new window.
Barkley, D. and Kevrekidis, I.G. (1994) ‘A dynamical systems approach to spiral-wave dynamicsLink opens in a new window’, Chaos, 4(3), pp. 453–460. doi:10.1063/1.166023Link opens in a new window.
Barkley, D. (1994) ‘Euclidean symmetry and the dynamics of rotating spiral wavesLink opens in a new window’, Physical Review Letters, 72(2), pp. 164–167. doi:10.1103/PhysRevLett.72.164Link opens in a new window.
Kness, M., Tuckerman, L.S. and Barkley, D. (1992) ‘Symmetry-breaking bifurcations in one-dimensional excitable mediaLink opens in a new window’, Physical Review A, 46(9), pp. 5054–5062. doi:10.1103/PhysRevA.46.5054Link opens in a new window.
Barkley, D. (1992) ‘Linear stability analysis of spiral waves in excitable mediaLink opens in a new window’, Physical Review Letters, 68(15), pp. 2090–2093. doi:10.1103/PhysRevLett.68.2090Link opens in a new window.
Barkley, D. (1991) ‘A model for fast computer simulation of waves in excitable mediaLink opens in a new window’, Physica D: Nonlinear Phenomena, 49(1–2), pp. 61–70. doi:10.1016/0167-2789(91)90194-ELink opens in a new window.
Tuckerman, L.S. and Barkley, D. (1990) ‘Bifurcation analysis of the Eckhaus instabilityLink opens in a new window’, Physica D: Nonlinear Phenomena, 46(1–2), pp. 57–86. doi:10.1016/0167-2789(90)90113-4Link opens in a new window.
Barkley, D. (1990) ‘Theory and predictions for finite-amplitude waves in two-dimensional plane Poiseuille flowLink opens in a new window’, Physics of Fluids A: Fluid Dynamics, 2(6), pp. 955–970. doi:10.1063/1.857603Link opens in a new window.
Lindberg, D., Turner, J.S. and Barkley, D. (1990) ‘Chaos in the Showalter-Noyes-BarEli model of the Belousov-Zhabotinskii reactionLink opens in a new window’, The Journal of Chemical Physics, 92(5), pp. 3238–3239. doi: 10.1063/1.457878Link opens in a new window.
Barkley, D., Kness, M. and Tuckerman, L.S. (1990) ‘Spiral-wave dynamics in a simple model of excitable media: The transition from simple to compound rotationLink opens in a new window’, Physical Review A, 42(5), pp. 2489–2492. doi:10.1103/PhysRevA.42.2489Link opens in a new window.
Barkley, D. and Cumming, A. (1990) ‘Thermodynamics of the quasiperiodic parameter set at the borderline of chaos: experimental resultsLink opens in a new window’, Physical Review Letters, 64(3), pp. 327–331. doi:10.1103/PhysRevLett.64.327Link opens in a new window.
Barkley, D. and Tuckerman, L.S. (1989) ‘Traveling waves in axisymmetric convection: the role of sidewall conductivityLink opens in a new window’, Physica D: Nonlinear Phenomena, 37(3), pp. 288–294. doi:10.1016/0167-2789(89)90136-XLink opens in a new window.
Barkley, D. (1988) ‘Near-critical behavior for one-parameter families of circle mapsLink opens in a new window’, Physics Letters A, 129(4), pp. 219–222. doi:10.1016/0375-9601(88)90353-2Link opens in a new window.
Tuckerman, L.S. and Barkley, D. (1988) ‘Global bifurcation to travelling waves in axisymmetric convectionLink opens in a new window’, Physical Review Letters, 61(4), pp. 408–411. doi:10.1103/PhysRevLett.61.408Link opens in a new window.
Barkley, D. (1988) ‘Slow manifolds and mixed-mode oscillations in the Belousov-Zhabotinskii reactionLink opens in a new window’, The Journal of Chemical Physics, 89(9), pp. 5547–5559. doi:10.1063/1.455561Link opens in a new window.
Barkley, D., Ringland, J. and Turner, J.S. (1987) ‘Observations of a torus in a model of the Belousov-Zhabotinskii reactionLink opens in a new window’, The Journal of Chemical Physics, 87(6), pp. 3812–3820. doi:10.1063/1.452937Link opens in a new window.