Papers

(Due to the shut down of Warwick unix servers, some of links below to pdf files do not work. I will fix this when I get a chance.)

Zuccoli, E., Brambley, E.J. and Barkley, D. (2024) 'A deep-water closure model for surface waves on axisymmetric swirling flows', (in review). https://arxiv.org/html/2405.12078v1Link 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 flow’, 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 elastomers’, 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 flow’, 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 flow’, 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 pipe’, 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 walls’, 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 flow’, 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 flows’, 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 waves’, 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 media’, Chaos, 23(1), p. 013134. doi:10.1063/1.4793783Link opens in a new window.
Barkley, D. (2012) ‘Pipe flow as an excitable medium’, Revista Cubana de Física, 29(1E), p. 27.
Barkley, D. (2011) ‘Modeling the transition to turbulence in shear flows’, Journal of Physics: Conference Series, 318, p. 032001.
Barkley, D. (2011) ‘Simplifying the complexity of pipe flow’, 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 flow’, 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 flow’, 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 wake’, Physics of Fluids, 23(1), p. 014104. doi:10.1063/1.3532839Link opens in a new window.
Cantwell, C.D. and Barkley, D. (2010) ‘Computational study of subcritical response in flow past a circular cylinder’, 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 functions’, 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 flow’, Proceedings of the National Academy of Sciences, 107(18), pp. 8091–8096. doi:10.1073/pnas.0911527107Link 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 convection’, 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 pipe’, Physics of Fluids, 22(3), p. 034101. doi:10.1063/1.3319071Link opens in a new window.
Biktashev, V.N., Barkley, D. and Biktasheva, I.V. (2010) ‘Orbital motion of spiral waves in excitable media’, 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 media’, 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 flows’, Journal of Fluid Mechanics, 607, pp. 267–277. doi:10.1017/S0022112008002036Link opens in a new window.
Barkley, D., Blackburn, H.M. and Sherwin, S.J. (2008) ‘Direct optimal growth analysis for timesteppers’, International Journal for Numerical Methods in Fluids, 57(9), pp. 1435–1458. doi:10.1002/fld.1872Link 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 step’, Journal of Fluid Mechanics, 603, pp. 271–304. doi:10.1017/S0022112008001106.
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 flow’, Journal of Fluid Mechanics, 576, pp. 109–137. doi:10.1017/S002211200600457XLink opens in a new window.
Barkley, D. (2006) ‘Linear analysis of the cylinder wake mean flow’, Europhysics Letters, 75(5), pp. 750–756. doi:10.1209/epl/i2006-10168-6Link 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 moments’, SIAM Journal on Applied Dynamical Systems, 5(3), pp. 403–434. doi:10.1137/050637231Link opens in a new window.
Wheeler, P. and Barkley, D. (2006) ‘Computation of spiral spectra’, SIAM Journal on Applied Dynamical Systems, 5(1), pp. 157–177. doi:10.1137/050641744Link opens in a new window.
Barkley, D. and Tuckerman, L.S. (2005) ‘Computational study of turbulent-laminar patterns in Couette flow’, 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 wake’, 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 flow’, in IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions. Fluid Mechanics and Its Applications, 77, pp. 107–127. doi:10.1007/1-4020-4049-8_12Link 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/s001620200103Link 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/S0022112002002382Link 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:10.1063/1.1485114Link 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)00170-1Link opens in a new window.
Duckett, G. and Barkley, D. (2000) ‘Modeling the dynamics of cardiac action potentials’, 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.61.5247.
Tuckerman, L.S. and Barkley, D. (2000) ‘Bifurcation analysis for timesteppers’, 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 method’, in Chattot, J.C. (ed.) 15th International Conference on Numerical Methods in Fluid Dynamics. Springer, New York.
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.54.4791.
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:10.1063/1.868958Link opens in a new window.
Barkley, D. (1995) ‘Spiral Meandering’, 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 media’, 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.