# Dr Christopher Davies

Reader

- daviesc9@cardiff.ac.uk
- +44 (0)29 2087 5531
- M/2.46, 2nd Floor, Mathematics Institute, Senghennydd Road, Cardiff, CF24 4AG

I am an active scientific researcher with interests in theoretical and computational fluid dynamics.

My main research interests are in:

- Hydrodynamic stability
- Vorticity-based numerical methods and formulations
- Fluid-structure interaction
- Rotating and oscillatory boundary layers

Much of my time is spent conducting and supervising research. But I also very much enjoy teaching applied mathematics, and communicating my enthusiasm for the subject to undergraduate students!

### Education

- BSc (Hons) Applied Mathematics, University of Warwick
- PGCE Secondary School Mathematics Teaching, University of Birmingham
- MSc Mathematics, University of Warwick
- PhD Engineering, University of Warwick

### Previous experience

- Intermediate Treatment Worker, Coventry & Warwickshire Social Services Departments
- Mathematics Tutor, Fircroft College of Adult Education, Birmingham
- Research Associate, School of Engineering, University of Warwick
- Research Fellow / Senior Lecturer, School of Mathematical and Information Sciences, Coventry University

### 2019

- Thomas, C. and Davies, C. 2019. Global linear instability of rotating-cone boundary layers in a quiescent medium. Physical Review Fluids 4, article number: 43902. (10.1103/PhysRevFluids.4.043902)

### 2018

- Thomas, C. and Davies, C. 2018. On the impulse response and global instability development of the infinite rotating-disc boundary layer. Journal of Fluid Mechanics 857, pp. 239-269. (10.1017/jfm.2018.748)
- Davies, C. and Thomas, C. 2018. Disturbance evolution in rotating boundary layers. Presented at: 21st Australasian Fluid Mechanics Conference, Adelaide, SA, Australia, 10-13 December 2018 Presented at Lau, T. C. W. and Kelso, R. M. eds.Proceedings of the 21st Australasian Fluid Mechanics Conference. Australasian Fluid Mechanics Society pp. -.

### 2017

- Davies, C. and Thomas, C. 2017. Global stability behaviour for the BEK family of rotating boundary layers. Theoretical and computational fluid dynamics 31(5-6), pp. 519-536. (10.1007/s00162-016-0406-9)

### 2016

- Davies, C., Thomas, C. and Ramage, A. 2016. Impulsively excited disturbances in non-uniform boundary layers. Presented at: 20th Australasian Fluid Mechanics Conference, University of Western Australia, Perth, Australia, December 2016Proceedings of the 20th Australasian Fluid Mechanics Conference. Australasian Fluid Mechanics Society

### 2015

- Davies, C.et al. 2015. The linear impulse response for disturbances in an oscillatory Stokes layer. Procedia IUTAM 14, pp. 381-384. (10.1016/j.piutam.2015.03.064)
- Thomas, C.et al. 2015. The linear stability of a Stokes layer subjected to high frequency perturbations. Journal of Fluid Mechanics 764, pp. 193-218. (10.1017/jfm.2014.710)
- Thomas, C., Hall, P. and Davies, C. 2015. Nonlinear effects on the receptivity of crossflow in the swept Hiemenz flow. Journal of Fluid Mechanics 763, pp. 433-459. (10.1017/jfm.2014.688)

### 2014

- Thomas, C.et al. 2014. Evolution of disturbance wavepackets in an oscillatory Stokes layer. Journal of Fluid Mechanics 752(Aug), pp. 543-571. (10.1017/jfm.2014.291)

### 2013

- Thomas, C. and Davies, C. 2013. Global stability of the rotating-disc boundary layer with an axial magnetic field. Journal of Fluid Mechanics 724, pp. 519-526. (10.1017/jfm.2013.162)

### 2012

- Duque-Daza, C.et al. 2012. Modelling turbulent skin-friction control using linearized Navier-Stokes equations. Journal of Fluid Mechanics 702, pp. 403-414. (10.1017/jfm.2012.189)

### 2011

- Thomas, C.et al. 2011. The linear stability of oscillatory Poiseuille flow in channels and pipes. Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences 467(2133), pp. 2643-2662. (10.1098/rspa.2010.0468)
- Togneri, M. and Davies, C. 2011. A high order finite-difference solver for investigation of disturbance development in turbulent boundary layers. Computers & Fluids 46(1), pp. 472-478. (10.1016/j.compfluid.2010.12.008)

### 2010

- Thomas, C., Bassom, A. P. and Davies, C. 2010. The linear stability of a Stokes layer with an imposed axial magnetic field. Journal of Fluid Mechanics 662, pp. 320-328. (10.1017/S0022112010004210)
- Davies, C. and Thomas, C. 2010. Disturbance evolution in rotating-disk boundary layers: competition between absolute instability and global stability. Presented at: 7th IUTAM Symposium on Laminar-Turbulent Transition, Stockholm, Sweden, 23-26 June 2009 Presented at Schlatter, P. and Henningson, D. S. eds.Seventh IUTAM Symposium on Laminar-Turbulent Transition: Proceedings of the Seventh IUTAM Symposium on Laminar-Turbulent Transition, Stockholm, Sweden, 2009. IUTAM Bookseries Vol. 18. London: Springer pp. 135-140., (10.1007/978-90-481-3723-7_20)
- Thomas, C.et al. 2010. Direct numerical simulations of small disturbances in the classical Stokes layer.. Journal of Engineering Mathematics 68(3-4), pp. 327-338. (10.1007/s10665-010-9381-0)
- Thomas, C. and Davies, C. 2010. The effects of mass transfer on the global stability of the rotating-disk boundary layer. Journal of Fluid Mechanics 663, pp. 401-433. (10.1017/S0022112010003563)

### 2009

- Sen, P. K.et al. 2009. A wave-driver theory for vortical waves propagating across junctions with application to those between rigid and compliant walls. Journal of Fluid Mechanics 625, pp. 1-46. (10.1017/S0022112008005545)

### 2007

- Davies, C., Thomas, C. and Carpenter, P. W. 2007. Global stability of the rotating-disk boundary layer. Journal of Engineering Mathematics 57(3), pp. 219-236. (10.1007/s10665-006-9112-8)
- Carpenter, P. W.et al. 2007. A deterministic model for the sublayer streaks in turbulent boundary layers for application to flow control. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 365(1859), pp. 2419-2441. (10.1098/rsta.2007.2016)
- Lockerby, D. A., Carpenter, P. W. and Davies, C. 2007. Is Helmholtz resonance a problem for micro-jet actuators?. Flow, Turbulence and Combustion 78(3-4), pp. 205-222. (10.1007/s10494-006-9056-0)
- Kudar, K. L., Carpenter, P. W. and Davies, C. 2007. An investigation into the evolution of sub-layer streaks in two- and three-dimensional turbulent boundary layers. Presented at: 11th EUROMECH European Turbulence Conference, Porto, Portugal, 25-28 June 2007 Presented at Palma, J. M. L. M. and Silva Lopes, A. eds.Advances in Turbulence XI: Proceedings of the 11th EUROMECH European Turbulence Conference, June 25-28, 2007, Porto, Portugal. Springer Proceedings in Physics Vol. 117. Dordrecht: Springer pp. 94-96.

### 2006

- Sen, P. K.et al. 2006. A wave-driver theory for vortical waves propagating across junctions between rigid and compliant walls. Presented at: 6th IUTAM Symposium on Laminar-Turbulent Transition, Bangalore, India, 2004 Presented at Govindarajan, R. ed.Sixth IUTAM Symposium on Laminar-Turbulent Transition: Proceedings of the Sixth IUTAM Symposium on Laminar-Turbulent Transition, Bangalore, India, 2004. Fluid Mechanics and Its Applications Vol. 78. Dordrecht: Springer pp. 195-200.
- Davies, C. 2006. Computational studies of boundary-layer disturbance development. Presented at: IUTAM Symposium on One Hundred Years of Boundary Layer Research, Göttingen, Germany, 12-14 August 2004 Presented at Meier, G. E. A., Screenivasan, K. R. and Heinemann, H. eds.IUTAM Symposium on One Hundred Years of Boundary Layer Research: Proceedings of the IUTAM Symposium held at DLR-Göttingen, Germany, August 12-14, 2004. Solid Mechanics and Its Applications Vol. 129. Dordrecht: Springer pp. 325-334.
- Kudar, K., Carpenter, P. W. and Davies, C. 2006. Klebanoff modes in swept boundary layers. Presented at: 6th IUTAM Symposium on Laminar-Turbulent Transition, Bangalore, India, 2004 Presented at Govindarajan, R. ed.Sixth IUTAM Symposium on Laminar-Turbulent Transition: Proceedings of the Sixth IUTAM Symposium on Laminar-Turbulent Transition, Bangalore, India, 2004. Fluid Mechanics and Its Applications Vol. 78. Dordrecht: Springer pp. 167-172.
- Davies, C.et al. 2006. Disturbance development in boundary layers over compliant surfaces. Presented at: 6th IUTAM Symposium on Laminar-Turbulent Transition, Bangalore, India, 2004 Presented at Govindarajan, R. ed.Sixth IUTAM Symposium on Laminar-Turbulent Transition: Proceedings of the Sixth IUTAM Symposium on Laminar-Turbulent Transition, Bangalore, India, 2004. Fluid Mechanics and Its Applications Vol. 78. Dordrecht: Springer pp. 225-230.

### 2005

- Davies, C. 2005. Numerical simulation of boundary-layer disturbance evolution. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 363(1830), pp. 1109-1118. (10.1098/rsta.2005.1553)
- Lockerby, D. A., Carpenter, P. W. and Davies, C. 2005. Control of sub-layer streaks using microjet actuators. AIAA Journal 43(9), pp. 1878-1886.

### 2003

- Bowles, R. I., Davies, C. and Smith, F. T. 2003. On the spiking stages in deep transition and unsteady separation. Journal of Engineering Mathematics 45(3/4), pp. 227-245. (10.1023/A:1022677807035)
- Davies, C. and Carpenter, P. W. 2003. Global behaviour corresponding to the absolute instability of the rotating-disc boundary layer. Journal of fluid mechanics 486, pp. 287-329. (10.1017/S0022112003004701)
- Davies, C. 2003. Convective and absolute instabilities of flow over compliant walls. Presented at: IUTAM Symposium on Flow Past Highly Compliant Boundaries and in Collapsible Tubes, Warwick, UK, 26-30 March 2001 Presented at Carpenter, P. W. and Pedley, T. J. eds.Flow Past Highly Compliant Boundaries and in Collapsible Tubes: IUTAM Symposium held at the University of Warwick, Coventry, United Kingdom, 26-30 March 2001. Fluid Mechanics and its Applications Vol. 72. Dordrecht: Kluwer Academic Publishers pp. 69-93.

### 2002

- Carpenter, P. W., Lockerby, D. A. and Davies, C. 2002. Numerical simulation of the interaction of microactuators and boundary layers. AIAA Journal 40(1), pp. 67-73.

### 2001

- Davies, C. and Carpenter, P. W. 2001. A novel velocity-vorticity formulation of the Navier-Stokes equations with applications to boundary layer disturbance evolution. Journal of computational physics 172(1), pp. 119-165. (10.1006/jcph.2001.6817)
- Carpenter, P. W., Lucey, A. D. and Davies, C. 2001. Progress on the use of compliant walls for laminar-flow control. Journal of Aircraft 38(3), pp. 504-512.

I teach the following modules:

- MA3301 Applied Nonlinear Systems
- MA0235 Elementary Fluid Dynamics
- MA4003 Theoretical Fluid Dynamics

I also have the following teaching related administrative responsibilities:

- Cardiff MAGIC co-ordinator
- Year 4 tutor

#### Research achievements

One of the main achievements of my research to date has been the demonstration that, at least in theory, compliant surfaces may be designed so as to delay the transition between laminar and turbulent flow in a boundary layer to indefinitely large Reynolds numbers.

Another significant achievement was the derivation of a new velocity-vorticity formulation of the Navier-Stokes equations. This new formulation has proved to be particularly suitable for simulating the evolution and control of three-dimensional disturbances in boundary layers.

I have also shown that the absolute instability that is found in a family of rotating boundary layers does not give rise to a global form of linear instabilty in anything like the manner that was predicted by other researchers. The connection between the local and global behaviour has turned out to be far more subtle and interesting than had been anticipated.

Most recently, along with my research collaborators, I have discovered a completely unexpected family-tree structure in the spatial-temporal evolution of disturbances that are excited in oscillatory boundary layers.

#### Research group

Applied and Computational Mathematics Research Group

#### Research grants

### European Commission

*Aeromems : An investigation into the viability of MEMS technology for boundary-layer control on aircraft*; 140,000 ECU, 1998-2000; Collaboration with Prof. Peter Carpenter, University of Warwick

### Engineering and Physical Sciences Research Council

*Near-wall flow structures in 3D turbulent boundary layers*; £330,000, 2005-2008; Collaboration with Prof. Peter Carpenter, University of Warwick; Two separate grants, one held at the University of Warwick and the other at Cardiff University

*Novel passive techniques for reducing skin-friction drag*; £186,000, 2007-2008; Collaboration with Prof. Peter Carpenter, University of Warwick

*Numerical simulation of transitional boundary-layer flows*; £5000, 2005-2006

*Investigation of alternative drag-reduction strategies in turbulent boundary layers using wall forcing*; £377,000, 2009-2012; Collaboration with Prof. Duncan Lockerby and others from the University of Warwick

*UK Fluids Network, Special Interest Group for Boundary Layers in Complex Rotating Systems*; £12,000, 2016-2019; Co-leader with Prof. Stephen Garrett, University of Leicester*Bridging the Gaps*; £47,000, 2012-2013; Co-organiser with colleagues from Cardiff Schools of Engineering, Computer Science, Psychology & Business School; Grant to promote interdisciplinary aerospace research

### Australian Research Council

*The stability of unsteady flows in channels and pipes*; $255,000, 2008-2010; Collaboration with Prof Andrew Bassom, University of Western Australia and Dr Peter Blennerhassett, University of New South Wales

### Royal Society

*India-UK Science Networks*; £4000, 2004

### Current supervision

## Martina Cracco

Research student