Biography

My research interests are in fluid dynamics and mathematical modelling, in particular using mathematics to model, understand and make predictions about practical problems arising from industry and other scientific disciplines.  My research uses combined asymptotic and numerical techniques, exploiting small parameters to reduce the complexity of the models studied.  

One long-term research interest is in droplet (and solid) impacts into water, and subsequent splashing. Originally motivated by predicting ice formation on aircraft during flight in clouds, my research has tried to improve predictions of splashing and water entry.  Recently, I have been interested in the influence of air effects, such as pre-impact air cushioning and how air influences the post-impact splash development.

Other ongoing research includes boundary-layer flow past multiple aerofoils and ground effects, the fluid mechanics of digestion and the stomach, and flow in elastic channels. 

I am actively involved in the UK Industrial Mathematics community.  I regularly attend Mathematical Study Groups with Industry, and organised the 85th European Study group with Industry at UEA in 2012.  I am also on the Scientific Committee of the Industrial Mathematics Knowledge Transfer Network.

Follow this link for details of current PhD opportunities in Mathematics. But feel free to email me to discuss projects outside these areas and alternative sources of funding.

Career History

  • Senior Lecturer, School of Mathematics, UEA. 2013-Present.
  • Lecturer, School of Mathematics, UEA. 2005-2013.
  • Research Associate, Rotorcraft and Aircraft Icing team, QinetiQ, Farnborough.  Under EPSRC RAIS Scheme, 2004-2005
  • Postdoc Researcher, University College London, 2003-2004Temporary Lecturer, University College London, 2002-2003
  • PhD, Rotor blades and ground effects, UCL, 2002

All Publications

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Purvis, R., Smith, F.

(2016)

Improving Aircraft Safety in Icing Conditions,

in UK Success Stories in Industrial Mathematics.

Springer International Publishing

UEA Repository

(Chapter)

(Published)


Deacon, N., Parau, E., Purvis, R., Whittaker, R.

(2015)

Nonlinear flexural waves in fluid–filled elastic channels,

in Journal of Fluids and Structures

52

pp. 16-36

Full Text UEA Repository

(Article)

(Published)


Rickett, L., Penfold, R., Blyth, M., Purvis, R., Cooker, M.

(2015)

Incipient mixing by Marangoni effects in slow viscous flow of two immiscible fluid layers,

in IMA Journal of Applied Mathematics

80

(5)

pp. 1582-1618

Full Text UEA Repository

(Article)

(Published)


Hicks, P., Purvis, R.

(2015)

Gas-cushioned droplet impacts with a thin layer of porous media,

in Journal of Engineering Mathematics

Full Text UEA Repository

(Article)

(Published)


Tsai, P., Wang, C., Wang, A., Korobkin, A., Purvis, R., Khabakhpasheva, T.

(2015)

Investigation of droplet oscillation on a vibrating elastic plate,

UEA Repository

(Paper)

(Published)


Kirby, S., Purvis, R.

(2013)

High-Reynolds-number flow past many blades in extreme ground effect,

in Quarterly Journal of Mechanics and Applied Mathematics

66

(2)

pp. 165-184

Full Text UEA Repository

(Article)

(Published)


Kirby, S., Purvis, R.

(2013)

Interactive planar multi-blade flows with a global angle of attack,

in European Journal of Mechanics - B/Fluids

41

pp. 150-162

Full Text UEA Repository

(Article)

(Published)


Hicks, P. D., Purvis, R.

(2013)

Liquid–solid impacts with compressible gas cushioning,

in Journal of Fluid Mechanics

735

pp. 120-149

Full Text UEA Repository

(Article)

(Published)


Hicks, P., Ermanyuk, E., Gavrilov, N., Purvis, R.

(2012)

Air trapping at impact of a rigid sphere onto a liquid,

in Journal of Fluid Mechanics

695

pp. 310-320

Full Text UEA Repository

(Article)

(Published)


Hicks, P., Purvis, R.

(2012)

Compressible air cushioning in liquid-solid impacts,

in Proceedings of the 2nd International Conferenceon Violent Flows

UEA Repository

(Article)

(Published)


Hicks, P., Purvis, R.

(2011)

Air cushioning in droplet impacts with liquid layers and other droplets,

in Physics of Fluids

23

(6)

pp. 062104

Full Text UEA Repository

(Article)

(Published)


Hicks, P., Purvis, R.

(2010)

Air cushioning and bubble entrapment in three-dimensional droplet impacts,

in Journal of Fluid Mechanics

649

pp. 135

Full Text UEA Repository

(Article)

(Published)


Hopkins, J., Evans, M., Lee, J., Lewis, A., Marsham, J., McQuaid, J., Parker, D., Stewart, D., Reeves, C., Purvis, R.

(2009)

Direct estimates of emissions from the megacity of Lagos,

in Atmospheric Chemistry and Physics

9

(21)

pp. 8471-8477

Full Text UEA Repository

(Article)

(Published)


Purvis, R., Johnson, E. R., Smith, F. T.

(2006)

Underbody and ground effects on rotating disc flow: a global inviscid study.,

in European Journal of Mechanics - B/Fluids

25

(6)

pp. 923-938

Full Text UEA Repository

(Article)

(Published)


Quero, M., Hammond, D., Purvis, R., Smith, F.

(2006)

Analysis of super-cooled water droplet impact on a thin water layer and ice growth,

UEA Repository

(Paper)

(Published)


Bowles, R., Dennis, S., Purvis, R., Smith, F.

(2005)

Multi-branching flows from one mother tube to many daughters or to a network,

in Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

363

(1830)

pp. 1045-1055

Full Text UEA Repository

(Article)

(Published)


Hammond, D., Quero, M., Ivey, P., Miller, D., Purvis, R., McGregor, O., Tan, J.

(2005)

Analysis and experimental aspects of the impact of supercooled water droplets into thin water films,

UEA Repository

(Paper)

(Published)


Howison, S. D., Ockendon, J. R., Oliver, J. M., Purvis, R., Smith, F. T.

(2005)

Droplet impact on a thin fluid layer,

in Journal of Fluid Mechanics

542

pp. 1-23

Full Text UEA Repository

(Article)

(Published)


Smith, F., Ovenden, N., Purvis, R.

(2005)

Industrial and Biomedical Applications, "One hundred years of boundary layer research",

UEA Repository

(Paper)

(Published)


Smith, F., Purvis, R.

(2005)

Air effects on droplet impact,

UEA Repository

(Paper)

(Published)


<- Page 1 of 2 ->

Key Research Interests

Impacts, violent flows and splashing: Using local asymptotic models to predict small-time behaviour just before and just after droplet/solid impacts.  A particular focus is on the influence of air on splashing; how does it cushion the impact before touchdown and how does air trigger splashing post impact?  Experimental evidence suggests that bubble trapping before impact, and air effects after impact, are vital in understanding the mechanisms present during splashing. Trying to answer these questions using 2D and 3D asymptotic models, coupled to numerical solutions. 

Aircraft Icing: How do droplet impacts and splashing influence ice growth on an aircraft during flight?  Experimentally it is known that splashing changes amount of ice formed and, more seriously, can cause ice to form in different (maybe unprotected) places.  Also trying to understand how rivulets form in runback ice on a wing, and how local conditions influence the structure and strength of the ice formed. 

High Reynolds-number flow past multiple aerofoils and ground effects:  Although flow past one aerofoil is well studied and understood, flow past several sequential aerofoils is less understood.  This work uses coupled viscous-inviscid models to investigate sheltering effects and upstream influence.  With multiple aerofoils, the viscous boundary layer part of the solution is coupled to the outer inviscid flow.  For 2D planar flows this has been investigated and solved, but an open problem remains to solve this coupled viscous-inviscid problem for a rotor blade. 

Mathematical Modelling: Other ongoing research includes the fluid mechanics of digestion in the stomach (joint work with Institute of Food Research), effects of pinching on explosives (joint with industry, motivated by safe handling of explosives), and fluid flow in elastic channels.

Research Keywords:

Droplet impacts and splashing

Air cushioning

High Reynolds number flows

Aircraft Icing

Asymptotic analysis

Mathematical Biology

Mathematical modelling

Industrial Mathematics



PGR Supervision:

Air cushioning in violent impacts

Splashing

Flow past multiple aerofoils

Aircraft Icing

Mathematical modelling/industrial mathematics

Rivulet formation in runback ice

Teaching Interests

Richard has taught a wide-range of undergraduate courses across all years of the degree programme.  These include lecturing:

Level 4: Calculus, and Multivariable Calculus, and introductions to Latex, Maple, Matlab and programming

Level 5: Differential Equations, Mathematical modelling, Fluid Mechanics, and Maths for Scientists

Level 6: Electricity and Magnetism, and Fluid Dynamics (plus level 7 versions of both with advanced topics)

Richard has also supervised several BSc projects, and many MMTH projects.

 

Professional Activities

  • Former Member of the scientific committee of the Industrial Mathematics Knowledge Transfer Network from 2007 until it was disbanded in 2013.
  • Organiser of the 85th Mathematical Study Group with Industry.2012

Key Responsibilities

  • Director of Admissions
  • IMA Departmental Representative for UEA
  • Previously: Deputy Director of Admissions, Director of Enterprise, CIMR research coordinator, Senior Advisor, Disability Liaison Officer,  Chair of MTH Extenuating Circumstances Panel,  Staff-Student Liaison Officer, London Technology Network Business Fellow.