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I made some videos explaining some of my recent research:

These were recorded while visiting Steve Brunton's lab.


Analytic solutions for flows through cascades

Springer, 2020 (link)

My PhD thesis was kindly published as a book by Springer. In the thesis, I use and develop techniques from complex variable theory to study idealised flows through cascades (periodic array of objects). These fluids problems are relevant to turbomachinery aeroacoustics and aerodynamics in addition to natural scenarios such as fish schooling. Most of the chapters from the thesis have been published individually in the papers below. The thesis also jointly won the "Best Thesis Award" from the UK Fluids Network.

The unpublished thesis can be downloaded here.



  • 2021: "Physics-informed dynamic mode decomposition" (link, video)
    P. J. Baddoo, B. Herrmann, B. J. McKeon, J. N. Kutz & S. L. Brunton


Streamlines on a multiply connected, periodic Riemann surface

Journal papers:


  • "Generalization of waving-plate theory to multiple interacting swimmers" (link, video)
    P. J. Baddoo N. J. Moore, A. U. Oza & D. G. Crowdy
    accepted at Communications on Pure and Applied Mathematics

  • "Kernel Learning for Robust Dynamic Mode Decomposition: Linear and Nonlinear Disambiguation Optimization (LANDO)" (link, video abstract)
    P. J. Baddoo, B. Herrmann, B. J. McKeon & S. L. Brunton
    Proceedings of the Royal Society A, 478:20210830, 2022



  • "Log-lightning computation of capacity and Green's function" (link, video abstract)
    P. J. Baddoo & L. N. Trefethen
    Maple Transactions, 1(1), 2021


  • "The AAAtrig algorithm for rational approximation of periodic functions" (link)
    P. J. Baddoo

    SIAM Journal of Scientific Computing, 43(5):A3372–A3392, 2021
    Note: AAAtrig is now available as part of Chebfun


  • "Data-driven resolvent analysis" (link, video abstract)
    B. Herrmann, P. J. Baddoo, R. Semaan, S. L. Brunton & B. J. McKeon
    Journal of Fluid Mechanics, 918:A10, 2021


  • "Unsteady aerodynamics of porous aerofoils" (link, code)
    P. J. Baddoo, R. Hajian & J. W. Jaworski
    Journal of Fluid Mechanics, 913:A16, 2021


  • "A calculus for flows in periodic domains" (link, code)
    P. J. Baddoo & L. J. Ayton
    Theoretical and Computational Fluid Dynamics, 35:145–168, 2021


  • "Lightning solvers for potential flows" (link)
    P. J. Baddoo
    Fluids, 5(4), 2020, (featured paper)

  • "Acoustic scattering by cascades with complex boundary conditions:
    compliance, porosity and impedance" (
    P. J. Baddoo & L. J. Ayton
    Journal of Fluid Mechanics, 898:A16, 2020


  • "Exact solutions for ground effect" (link, code, video abstract)
    P. J. Baddoo, M. Kurt, L. J. Ayton & K. W. Moored
    Journal of Fluid Mechanics Rapids, 891:R2 2020


  • "An analytic solution for gust–cascade interaction noise including effects of
    realistic aerofoil geometry" (
    P. J. Baddoo & L. J. Ayton
    Journal of Fluid Mechanics, 886:A1, 2020



  •  "Periodic Schwarz–Christoffel mappings with multiple boundaries per period"
    linkvideo abstract)

    P. J. Baddoo & D. G. Crowdy
    Proceedings of the Royal Society A, 475:20190225, 2019 (featured paper)



  • "Potential flow through a cascade of aerofoils: direct and inverse problems" (link)

    P. J. Baddoo & L. J. Ayton
    Proceedings of the Royal Society A, 474:20180065, 2018



  • "Electron bunch profile reconstruction based on phase-constrained iterative
    algorithm" (

    F. Bakkali Taheri, I.V. Konoplev, G. Doucas, P. J. Baddoo, R. Bartolini, J. Cowley
    & S.M. Hooker,
    Physical Review Accelerators and Beams, 19(3), 2016


Idealised flow past a complicated boundary with embedded vortices

Pressure fields around a pair of heaving plates

Featured article in Proceedings of the Royal Society A

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