Dwight Barkley

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Dwight Barkley (born 7 January 1959) [1] is a professor of mathematics at the University of Warwick. [2] [3]

Contents

Education and career

Barkley obtained his PhD in physics from the University of Texas at Austin in 1988. [4] He then spent one year at Caltech working with Philip Saffman followed by three years at Princeton University where he worked with Yannís Keverkidis and Steven Orszag. In 1992 he was awarded both NSF and NATO postdoctoral fellowships. [4] In 1994 he joined the faculty at the University of Warwick.

Research

Barkley studies waves in excitable media such as the Belousov–Zhabotinsky reaction, heart tissue, and neurons. He is the author of the Barkley Model of excitable media [5] [6] and discoverer of the role of Euclidean symmetry in spiral-wave dynamics. [7]

In 1997, Laurette Tuckerman and Dwight Barkley coined the term "bifurcation analysis for time steppers" for techniques involving the modification of time-stepping computer codes to perform the tasks of bifurcation analysis. [8] He has applied this approach in several areas of fluid dynamics, in particular to stability analysis of the cylinder wake [9] and of the backward-facing step. [10]

Barkley also works on the transition to turbulence in shear flows, including the formation of turbulent-laminar bands [11] [12] and the critical point for pipe flow. [13] [14] Exploiting an analogy with the transition between excitable and bistable media, Barkley derived a model for pipe flow which captures most features of transition to turbulence, in particular the behavior of turbulent regions called puffs and slugs. [15] [16]

He is also known for deriving an equation to estimate how long it will be until a child in a car asks the question "are we there yet?" [17]

Awards

In 2005 he was awarded the J. D. Crawford Prize for outstanding research in nonlinear science, "for his development of high quality, robust and efficient numerical algorithms for pattern formation phenomena in spatially extended dynamical systems". [18] [19]

In 2008 he was elected Fellow of the American Physical Society "for combining computation and dynamical systems analyses to obtain remarkable insights into hydrodynamic instabilities and patterns in diverse systems, including flow past a cylinder, channel flow, laminar-turbulent bands, and thermal convection." [20] That same year he was also elected fellow of the Institute of Mathematics and Its Applications. [4]

In 2009-2010 he was a Royal Society–Leverhulme Trust Senior Research Fellow. [21]

In 2016 he was elected Fellow of the Society for Industrial and Applied Mathematics "For innovative combinations of analysis and computation to obtain fundamental insights into complex dynamics of spatially extended systems." [22]

Selected publications

Related Research Articles

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In fluid dynamics, laminar flow is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow, the motion of the particles of the fluid is very orderly with particles close to a solid surface moving in straight lines parallel to that surface. Laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection.

In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers.

Quantum turbulence is the name given to the turbulent flow – the chaotic motion of a fluid at high flow rates – of quantum fluids, such as superfluids. The idea that a form of turbulence might be possible in a superfluid via the quantized vortex lines was first suggested by Richard Feynman. The dynamics of quantum fluids are governed by quantum mechanics, rather than classical physics which govern classical (ordinary) fluids. Some examples of quantum fluids include superfluid helium, Bose–Einstein condensates (BECs), polariton condensates, and nuclear pasta theorized to exist inside neutron stars. Quantum fluids exist at temperatures below the critical temperature at which Bose-Einstein condensation takes place.

<span class="mw-page-title-main">Nonlinear Schrödinger equation</span> Nonlinear form of the Schrödinger equation

In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation. It is a classical field equation whose principal applications are to the propagation of light in nonlinear optical fibers and planar waveguides and to Bose–Einstein condensates confined to highly anisotropic, cigar-shaped traps, in the mean-field regime. Additionally, the equation appears in the studies of small-amplitude gravity waves on the surface of deep inviscid (zero-viscosity) water; the Langmuir waves in hot plasmas; the propagation of plane-diffracted wave beams in the focusing regions of the ionosphere; the propagation of Davydov's alpha-helix solitons, which are responsible for energy transport along molecular chains; and many others. More generally, the NLSE appears as one of universal equations that describe the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear media that have dispersion. Unlike the linear Schrödinger equation, the NLSE never describes the time evolution of a quantum state. The 1D NLSE is an example of an integrable model.

<span class="mw-page-title-main">Taylor–Couette flow</span>

In fluid dynamics, the Taylor–Couette flow consists of a viscous fluid confined in the gap between two rotating cylinders. For low angular velocities, measured by the Reynolds number Re, the flow is steady and purely azimuthal. This basic state is known as circular Couette flow, after Maurice Marie Alfred Couette, who used this experimental device as a means to measure viscosity. Sir Geoffrey Ingram Taylor investigated the stability of Couette flow in a ground-breaking paper. Taylor's paper became a cornerstone in the development of hydrodynamic stability theory and demonstrated that the no-slip condition, which was in dispute by the scientific community at the time, was the correct boundary condition for viscous flows at a solid boundary.

<span class="mw-page-title-main">Turbulence modeling</span> Use of mathematical models to simulate turbulent flow

In fluid dynamics, turbulence modeling is the construction and use of a mathematical model to predict the effects of turbulence. Turbulent flows are commonplace in most real-life scenarios, including the flow of blood through the cardiovascular system, the airflow over an aircraft wing, the re-entry of space vehicles, besides others. In spite of decades of research, there is no analytical theory to predict the evolution of these turbulent flows. The equations governing turbulent flows can only be solved directly for simple cases of flow. For most real-life turbulent flows, CFD simulations use turbulent models to predict the evolution of turbulence. These turbulence models are simplified constitutive equations that predict the statistical evolution of turbulent flows.

<span class="mw-page-title-main">Eddy (fluid dynamics)</span> Swirling of a fluid and the reverse current created when the fluid is in a turbulent flow regime

In fluid dynamics, an eddy is the swirling of a fluid and the reverse current created when the fluid is in a turbulent flow regime. The moving fluid creates a space devoid of downstream-flowing fluid on the downstream side of the object. Fluid behind the obstacle flows into the void creating a swirl of fluid on each edge of the obstacle, followed by a short reverse flow of fluid behind the obstacle flowing upstream, toward the back of the obstacle. This phenomenon is naturally observed behind large emergent rocks in swift-flowing rivers.

<span class="mw-page-title-main">Intermittency</span> Irregular alternation different types of dynamics

In dynamical systems, intermittency is the irregular alternation of phases of apparently periodic and chaotic dynamics, or different forms of chaotic dynamics.

<span class="mw-page-title-main">Law of the wall</span> Relation of flow speed to wall distance

In fluid dynamics, the law of the wall states that the average velocity of a turbulent flow at a certain point is proportional to the logarithm of the distance from that point to the "wall", or the boundary of the fluid region. This law of the wall was first published in 1930 by Hungarian-American mathematician, aerospace engineer, and physicist Theodore von Kármán. It is only technically applicable to parts of the flow that are close to the wall, though it is a good approximation for the entire velocity profile of natural streams.

Harry L. Swinney is an American physicist noted for his contributions to the field of nonlinear dynamics.

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In continuum mechanics, wave turbulence is a set of nonlinear waves deviated far from thermal equilibrium. Such a state is usually accompanied by dissipation. It is either decaying turbulence or requires an external source of energy to sustain it. Examples are waves on a fluid surface excited by winds or ships, and waves in plasma excited by electromagnetic waves etc.

Robert Harry Kraichnan, a resident of Santa Fe, New Mexico, was an American theoretical physicist best known for his work on the theory of fluid turbulence.

In fluid mechanics, pipe flow is a type of liquid flow within a closed conduit, such as a pipe or tube. The other type of flow within a conduit is open channel flow. These two types of flow are similar in many ways, but differ in one important aspect. Pipe flow does not have a free surface which is found in open-channel flow. Pipe flow, being confined within closed conduit, does not exert direct atmospheric pressure, but does exert hydraulic pressure on the conduit.

<span class="mw-page-title-main">Philip Saffman</span> British mathematician (1931–2008)

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References

  1. ↑ Barkley, Dwight. (September 2019). Curriculum vitae. University of Warwick.
  2. ↑ "Home page for Dwight Barkley". 4 October 2011. Retrieved 16 September 2015.
  3. ↑ "Dwight Barkley". scholar.google.com. Retrieved 14 September 2023.
  4. 1 2 3 "Dwight Barkley - ORCID". Orcid. Retrieved 14 September 2023.
  5. ↑ Barkley, Dwight (1991). "A model for fast computer simulation of waves in excitable media". Physica D: Nonlinear Phenomena. 49 (1–2): 61–70. Bibcode:1991PhyD...49...61B. doi:10.1016/0167-2789(91)90194-E.
  6. ↑ Barkley, Dwight (2008). "Barkley model". Scholarpedia. 3 (11): 1877. Bibcode:2008SchpJ...3.1877B. doi: 10.4249/scholarpedia.1877 .
  7. ↑ Barkley, Dwight (1994). "Euclidean symmetry and the dynamics of rotating spiral waves". Physical Review Letters. 72 (1): 164–167. Bibcode:1994PhRvL..72..164B. doi:10.1103/PhysRevLett.72.164. PMID   10055592.
  8. ↑ Tuckerman, Laurette S.; Barkley, Dwight (1998). "Bifurcation analysis for timesteppers". University of Minnesota digital conservancy. Retrieved 16 September 2015.
  9. ↑ Barkley, Dwight; Henderson, Ronald D. (2006). "Three-dimensional Floquet stability analysis of the wake of a circular cylinder". Journal of Fluid Mechanics. 322 (1): 215–241. Bibcode:1996JFM...322..215B. doi:10.1017/S0022112096002777. S2CID   53610776.
  10. ↑ Barkley, Dwight; Gomes, M. Gabriela M.; Henderson, Ronald D. (2002). "Three-dimensional instability in flow over a backward-facing step" (PDF). Journal of Fluid Mechanics. 473 (1): 167–190. Bibcode:2002JFM...473..167B. doi:10.1017/S002211200200232X. S2CID   54012009.
  11. ↑ Barkley, Dwight; Tuckerman, Laurette S. (2005). "Computational Study of Turbulent Laminar Patterns in Couette Flow". Physical Review Letters. 94 (1): 014502. arXiv: physics/0403142 . Bibcode:2005PhRvL..94a4502B. doi:10.1103/PhysRevLett.94.014502. PMID   15698087. S2CID   40340539.
  12. ↑ Tuckerman, Laurette S.; Chantry, Matthew; Barkley, Dwight (2020). "The Patterns in Wall-Bounded Shear Flows" (PDF). Annual Review of Fluid Mechanics. 52: 343–367. Bibcode:2020AnRFM..52..343T. doi:10.1146/annurev-fluid-010719-060221. S2CID   202155000.
  13. ↑ Avila, K.; Moxey, D.; de Lozar, A.; Avila, M.; Barkley, D.; Hof, B. (2011). "The Onset of Turbulence in Pipe Flow". Science. 333 (6039): 192–196. Bibcode:2011Sci...333..192A. doi:10.1126/science.1203223. PMID   21737736. S2CID   22560587.
  14. ↑ Avila, Marc; Barkley, Dwight; Hof, Bjorn (2023). "Transition to Turbulence in Pipe Flow" (PDF). Annual Review of Fluid Mechanics. 55: 575–602. Bibcode:2023AnRFM..55..575A. doi:10.1146/annurev-fluid-120720-025957.
  15. ↑ Barkley, Dwight (2011). "Simplifying the complexity of pipe flow". Physical Review E. 84 (1 Pt 2): 016309. arXiv: 1101.4125 . Bibcode:2011PhRvE..84a6309B. doi:10.1103/PhysRevE.84.016309. PMID   21867306. S2CID   16527841.
  16. ↑ Barkley, Dwight (2016). "Theoretical perspective on the route to turbulence in a pipe" (PDF). Journal of Fluid Mechanics. 803: P1. Bibcode:2016JFM...803P...1B. doi:10.1017/jfm.2016.465. S2CID   123707242.
  17. ↑ "Kids' car question put in formula", BBC News , 20 July 2006
  18. ↑ "J.D. Crawford Prize". SIAM . Retrieved 20 May 2015.
  19. ↑ "UK Nonlinear News Issue 40". www1.maths.leeds.ac.uk. Retrieved 14 September 2023.
  20. ↑ "Home - Unit - DFD" (PDF).
  21. ↑ "News 2010". warwick.ac.uk. Retrieved 14 September 2023.
  22. ↑ "Fellows Program | SIAM". www.siam.org. Retrieved 14 September 2023.
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