Rich Kerswell

DAMTP
Centre for Mathematical Sciences
University of Cambridge
Wilberforce Rd
Cambridge CB3 0WA, U.K.

R.R.Kerswell@damtp.cam.ac.uk

Tel: +44-1223-766349

https://www.damtp.cam.ac.uk/user/rrk26/

Research Interests

The Navier-Stokes equations (nonlinear dynamics, transition and turbulence)
Geophysical and astrophysical fluid mechanics (e.g. convecting and stably-stratified flows,
tidal, precessional and librational motion of planetary interiors and subsurface oceans, accretion disks)
Viscoelastic flows (elasto-inertial and elastic turbulence)
Machine learning & optimisation in fluid mechanics

Interested in a PhD with me?

here

Lecture notes

Woods Hole Oceanographic Institution GFD summer school: `Shear Turbulence: Onset and Structure' 20 June - 26 August 2011, Woods Hole, Massachusetts.
( Principal lectures: 1. Transition scenarios; 2. Edge tracking 3. Triggering turbulence efficiently (now updated in Rep. Prog. Phys. 77 , 085901, 2014); 4. Turbulence: transient or sustained? ) (hard at work).
CISM-ECCOMAS Summer school on 'Coherent Structures in Unsteady Flows: Mathematical and Computational Methods' June 3-7 2019, Udine, Italy
( Draft lectures on Exact Coherent Structures: 1. Theory & Methods; 2. Importance & Identification; 3. Variational Methods )

Recent Meetings

Mathematical Aspects of Geophysical and Astrophysical Fluid Dynamics (AMS80), Jan 11-12, 2024, Newcastle, UK.
ICTAM 2024, August 25-30, 2024, Daegu, South Korea.
IUTAM Transition 2024, September 2-6, 2024, Nagano, Japan.
Chaotic Flows in Polymer Solutions, January 6-10, 2025, Edinburgh, UK.
International Workshop of Multi-Scale, Multi-Media and Multi-Physics Rheology (M3Rheo 2025), August 11-14, 2025, Tianjin, China.
2nd European Fluid Dynamics Conference, August 26-29, 2025, Dublin, Ireland.
UK Fluids Conference 2025, September 2-4, 2025, Liverpool, UK.
APS DFD 2025, November 23-25, 2025, Houston, USA.

Papers:

Archive (selected):
Kerswell, R.R. ``The instability of precessing flow'' Geophys. Astrophys. Fluid Dynam. 72, 107-144, 1993.
Kerswell, R.R. ``Tidal excitation of hydromagnetic waves and their damping in the Earth'' J. Fluid Mech. 274, 219-241, 1994.
Kerswell, R.R. ``Secondary instabilities in rapidly rotating flows: inertial wave breakdown'' J. Fluid Mech. 382, 283--306, 1999.
Kerswell, R.R. ``Upper bounds on general dissipation functionals in turbulent shear flows: revisiting the `efficiency' functional'' J. Fluid Mech. 461, 239-275, 2002.
Wedin, H. & Kerswell, R.R. ``Exact coherent structures in pipe flow: travelling wave solutions'' (colour version) J. Fluid Mech. 508, 333-371, 2004.
Pringle, C.C.T., Duguet, Y. & Kerswell, R.R. ``Highly symmetric travelling waves in pipe flow''(colour version) Phil. Trans. Roy. Soc. A 367, 457-472, 2009 (TW videos).
Pringle, C.C.T. & Kerswell, R.R. ``Using nonlinear transient growth to construct the minimal seed for shear flow turbulence'' Phys. Rev. Lett. 105, 154502, 2010.
Chandler, G.J. & Kerswell, R.R. ``Simple invariant solutions embedded in 2D Kolmogorov turbulence'' J. Fluid Mech. 722, 554-595, 2013.
Kerswell, R.R. ``Nonlinear nonmodal stability theory'' Ann. Rev. Fluid Mech. 50, 319-345, 2018.
Page, J., Dubief, Y. & Kerswell, R.R. ``Exact travelling wave solutions in viscoelastic channel flow'' Phys. Rev. Lett. 125, 154501, 2020.
Page, J., Brenner, M.P. & Kerswell, R.R. ``Revealing the state space of turbulence using machine learning'' Phys. Rev. Fluids 6, 034402, 2021.
Buza, G., Beneitez, M., Page, J. & Kerswell, R.R. ``Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number" J. Fluid Mech. 951, A3, 2022.
Beneitez, M., Page, J. & Kerswell, R. R. ``Polymeric diffusive instability leading to elastic turbulence in plane Couette flow'' Phys. Rev. Fluids 8, L101901, 2023.

Recent:
Markeviciute, V.K. & Kerswell, R.R. ``Threshold transient growth as a criterion for turbulent mean profiles'' J. Fluid Mech. 996, A32, 2024.
Page, J., Norgaard, P., Brenner, M. P. & Kerswell, R. R. ``Recurrent flow patterns as a basis for turbulence: predicting statistics from structures'' Proc. Nat. Acad. Sci. 121, e2320007121, 2024.
Beneitez, M., Page, J., Dubief, Y. & Kerswell, R. R. ``Multistability of elasto-inertial two-dimensional channel flow'' J. Fluid Mech. 981, A30, 2024.
Couchman, M. M. P., Beneitez, M., Page, J. & Kerswell, R. R. ``Inertial enhancement of the polymer diffusive instability"J. Fluid Mech. 981, A2, 2024.
Page, J., Holey, J., Brenner, M. P. & Kerswell, R. R. ``Exact coherent structures in two-dimensional turbulence identified with convolutional autoencoders'' J. Fluid Mech. 991, A10, 2024.
Zhu, L., Jiang, X. , Lefauve, A., Kerswell, R. R. & Linden, P. F. ``New insights into experimental stratified flows obtained through Physics-informed neural networks" J. Fluid Mech. 981, R1, 2024.
Shokar, I. J. S., Kerswell, R. R. & Haynes, P. H. ``Stochastic latent transformer: efficient modelling of stochastically forced zonal jets'' J. Advances in Modelling Earth Systems (JAMES) 16, e2023MS004177, 2024.
Lewy, T. & Kerswell, R. R. ``The polymer diffusive instability in highly concentrated polymeric fluids'' J. Non Newton. Fluid Mech. 326, 105212, 2024.
Zhu, L., Atoufi, A., Lefauve, A., Kerswell, R. R. & Linden, P. F. ``Long-wave instabilities of sloping stratified exchange flows'' J. Fluid Mech. 983, A12, 2024.
Oxley, W. & Kerswell, R. R. ``Linear stability of stratified, rotating, viscous plane Couette-Poiseuille flow'' J. Fluid Mech. 991, A16, 2024.
Kerswell, R. R. & Page, J. ``Asymptotics of the centre mode instability in viscoelastic channel flow: with and without inertia'' J. Fluid Mech. 991, A13, 2024.
Lin, Y. & Kerswell, R. R. ``Weakening the effect of boundaries: `diffusion-free' boundary conditions as a `do least harm' alternative to Neumann" Geophys. Astrophys. Fluid Dyn. 1-25, https://doi.org/10.1080/03091929.2024.2403759, 2024.
Beneitez, M., Page, J., Dubief, Y. & Kerswell, R. R. ``Transition route to elastic and elasto-inertial turbulence in polymer channel flows'' Phys. Rev. Fluids. 9, 123303, 2024.
Madhusudanan, A. & Kerswell, R. R. ``Predicting bursting events in 2-D Kolmogorov flows: A wavelet-based analysis'' J. Fluid Mech. 1003, A5, 2025.
Nivarti, G. V., Kerswell, R. R., Marston, J. B. & Tobias, S. M. ``Non-equivalence of quasilinear dynamical systems and their statistical closures'' J. Fluid Mech. 1005, A5, 2025.
Cassia, R. & Kerswell, R. R. ``Godunov loss functions for modelling conservation laws'' Computer Methods in Applied Mechanics and Engineering 437, 117782, 2025.
Lewy, T. & Kerswell, R. R. ``Revisiting 2D viscoelastic Kolmogorov flow: a centre-mode-driven transition" J. Fluid Mech. 1007, A55, 2025.
Oxley, W. & Kerswell, R. R. ``Transient growth in streaky unbounded shear flow: a symbiosis of Orr and push-over mechanisms'' accepted in J. Fluid Mech.
Klingenberg, D. & Kerswell, R. R. "Nonlinear optimals and their role in sustaining turbulence in channel flow" J. Fluid Mech. 1015, A50, 2025.
Beneitez, M., Mrini, S. and Kerswell, R. R. "Linear instability in planar viscoelastic Taylor-Couette flow with and without explicit polymer diffusion'' J. Non Newton. Fluid Mech. 345, 105459, 2025.
Shokar, I. J. S., Haynes, P. H. & Kerswell, R. R. ``Deep learning of the evolution operator enables forecasting of out-of-training dynamics in chaotic systems''
Zhu, L. & Kerswell, R. R. ``Early turbulence in viscoelastic flow past a periodic cylinder array''
Lewy, T. A., Fielding, S. M., Olmsted, P. D. & Kerswell, R. R. " Elastic turbulence in highly entangled polymers and wormlike micelles''

Postdocs:

Ashley Willis, EPSRC-funded 2005-2008 (now Senior Lecturer at Sheffield University)
Yohann Duguet, Marie-Curie Fellow 2006-2008 (now CNRS, LIMSI, Paris)
Laurent Lacaze, Marie-Curie Fellow 2006-2008 (now CNRS, IMFT, Toulouse)
Mark Woodhouse, Renishaw & North Bristol NHS Trust funded 2007-2009 (now NERC Knowledge Exchange Fellow, Bristol University)
Gary Chandler, EPSRC-funded 2010-2011 (now Motorsport engineering)
Dan Lucas, EPSRC-funded 2012-2013 (now Lecturer at St Andrews University)
Colin Leclercq, EPSRC-funded 2014-2016 (now Ingenieur de Recherche, ONERA, Meudon)
Jacob Page, EPSRC-funded 2016-2018 (now Reader in Applied Mathematics, Edinburgh University)
Jake Langham, EPSRC Doctoral Prize 2017-2019 (now a postdoc with Prof Andrew Hogg at Bristol)
Zijing Ding, EPSRC-funded 2017-2020 (now Professor at the Harbin Institute of Technology, China) (genius)
Hadi Zolfaghari SNSF-funded & Marie-Curie Fellow 2020-2023 (now software engineer, Neubla, UK)
Miles Couchman DAMTP-funded (with C.P. Caulfield) 2020-2022 (now Assistant Professor at York University, Canada)
Lu Zhu ERC-funded (with P.F. Linden) 2021-2023 and Dec 2023-Apr 2025 (DAMTP-funded) (now postdocing at Edinburgh with Jacob Page)
Miguel Beneitez, EPSRC-funded (with J. Page, Edinburgh) 2021-2024 (now a Lecturer in Engineering, Manchester University)
Anagha Madhusudanan, INI-Simons Fellow Jan-Dec 2022 (now a 5-year INSPIRE fellow in Bengaluru)
Dario Klingenberg DAAD Scholar (German Academic Exchange) Sept 2023-Feb 2025 (now postdocing at ZARM, Univ. of Bremen with Marc Avila)
Fabio Pino, Wiener-Anspach Fellow Oct 2024-Sept 2026
Gergely Buza, DAMTP-funded Oct 2024-Mar 2025 (now postdocing at ETH with George Haller)

Graduate students:

Darren Mason 1995-1999 (now software engineering).
Denise Cooper (née Barnes) 1996-2000 (now senior software engineer at Radan Computational Ltd, Bath, in CAD).
Robert Mason 1998-2001 (now Serco Assurance, Dorchester, in scientific consultancy).
Stephen Plasting 2000-2004 (followed by a postdoc at Scripps Oceanographic Institute, San Diego with W.R. Young; now finance).
Hakan Wedin 2001-2004 (followed by postdocs at Kyoto University with M. Nagata and now Genoa University with A. Bottaro).
Chris Pringle 2005-2009 (followed by postdocs at Reading and Nottingham Universities, now Associate Professor at Coventry University).
Helen Sweeney 2008-2011 (followed by training with Teach First).
Samuel Rabin 2009-2013, co-supervised with C. Caulfield (now finance).
Matthew Chantry 2010-2014 (followed by postdocs in Paris and Oxford, now at ECMWF).
Daniel Olvera 2012-2016 (now a software engineer).
Jeremy Parker 2017-2020, co-supervised with C. Caulfield (now Lecturer at the University of Dundee).
Vilda Markeviciute 2018-2022 (EPSRC, now at Expedia)
Gergely Buza 2020-2024 (Harding Fellow, now postdocing at ETH)
Will Oxley 2020- (EPSRC, thesis submitted).
Joe Holey 2020-2025 (CMI) co-supervised with J. Page.
Ira Shokar 2021-2025 (AI4ER, now at Nvidia), co-supervised with P. Haynes
Rami Cassia 2021- (CMI).
Theo Lewy 2022- (Trust Fellow).
Ruben Dahan 2024- (EPSRC).