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

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.
2nd European Fluid Dynamics Conference, August 26-29, 2025, Dublin, Ireland.
UK Fluids Conference 2025, September 2-4, 2025, Liverpool, UK.

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 Newtonian 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.
Zhu, L. & Kerswell, R. R. ``Early turbulence in viscoelastic flow past a periodic cylinder array''
Oxley, W. & Kerswell, R. R. ``Transient growth in streakly unbounded shear flow: a symbiosis of Orr and push-over mechanisms''
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''
Klingenberg, D. & Kerswell, R. R. "Nonlinear optimals and their role in sustaining turbulence in channel flow"

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 Lecturer 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)
Miguel Beneitez, EPSRC-funded (with J. Page, Edinburgh) 2021-2024 (currently a postdoc at KTH before joining Dept. of Engineering, Manchester University in April 2025)
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 ZARM, Univ. of Bremen)
Fabio Pino, Wiener-Anspach Fellow Oct 2024-Sept 2026
Gergely Buza, DAMTP-funded Oct 2024-Mar 2025

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 in DAMTP)
Will Oxley 2020- (EPSRC).
Joe Holey 2020- (CMI) co-supervised with J. Page.
Ira Shokar 2021- (AI4ER), co-supervised with P. Haynes.
Rami Cassia 2021- (CMI).
Theo Lewy 2022- (Trust Fellow).
Ruben Dahan 2024- (EPSRC).