I am a mathematician and engineer working on fundamental engineering problems. My interests span turbulent stratified mixing and fluid-structure interactions.

Currently, I am a postdoc researcher for Managing Air for Green Inner Cities (MAGIC), examining the interaction between building ventilation systems and their surroundings, at the Department for Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge.

I was previously a Courant Instructor at the Applied Mathematics Laboratory, based in the Courant Institute, New York University, where I was also a Fulbright Scholar. There I investigated the interaction between a dissolving body and a buoyancy-driven flow and flow-structure interaction at the microscale.

My PhD was on turbulent stratified mixing and the Rayleigh-Taylor instability, supervised by Dr Stuart Dalziel. I did this research at DAMTP, University of Cambridge.

DAMTP,

Centre for Mathematical Sciences,

Wilberforce Road,

Cambridge,

CB3 0WA,

United Kingdom

+44 (1223) 764053

**Curriculum Vitae** PDF

To efficiently and effectively ventilate buildings, we need to understand the flows inside them. Cooling buildings using air conditioning requires a large amount of energy. However, this is not the only way to cool buildings - we can also make use of the natural forces of wind and buoyancy to ventilate and cool spaces. This is known as natural ventilation.

I research the ways that wind and buoyancy interact in naturally ventilated buildings. I am particularly interested in how buoyancy modifies wind-driven cross-ventilation. This research uses laboratory experiments, computational simulations, and field measurements to build simple models and develop rules of thumb that can be used to design and improve ventilation systems.

When the roads are wet, vehicle wheels can pick up water from the road and spray it out behind the wheel. Not only is this a nuisance to cyclists, it can also represent a hazard as the spray can result in mist, reducing visibility in wet conditions, increasing the likelyhood of an accident.

Understanding how wheels entrain and emit fluid could help us to identify ways of reducing splash and spray from wheels, by designing better shielding and alternative road surfacing. I have investigated the spash thrown out by a partially submerged rotating wheel.

Turbulent stratfied mixing is a fundamental problem in fluid dynamics. Models of how heat is mixed into the ocean are needed to predict the magnitude of sea level rise due to climate change. I have studied turbulent stratified mixing in the context of the Rayleigh-Taylor instability, which occurs at an interface between two fluids of different densities, where the dense fluid is accelerated into the less dense fluid. My research examined the mixing that occurs when Rayleigh-Taylor instability is between two otherwise stably-stratified layers. I discovered that high values of the mixing efficiency (more than 70%) are possible (see pdf). These results led to new insights into mixing in unstably stratified flows (see pdf).

A video of this instability can be found on YouTube.

Swimming at the micro-scale looks very different to the swimming of fish or humans. The low Reynolds number means standard swimming strategies will not work. To design low Reynolds number swimmers that can perform useful tasks, we need to discover new strategies for assembling and steering micro-scale swimmers.

Artificial micron-scale swimmers can be created by placing metallic rods in a chemical fuel. I have shown that diffusive rods can be made to self-assemble into structures with the two fundamental types of directed motion, rotors and T-shaped swimmers (see arXiv). I have also discovered a new method for steering micro-scale swimmers, using the geometry of their environment (see arXiv).

Many of the shapes around us are formed from the interaction between a flow and an evolving object, from snowflakes and icicles to stalactites and river meanders. The effect a flow has on the shape of an object depends on the details of the interaction. I discovered that dissolving objects can retain memory of their initial shape if the surrounding flow is gravitationally unstable and the length-scale of this instability is much smaller than the size of the object. However, if the flow is stable, all memory of initial conditions can be wiped away (see paper).

A video of a candy sphere dissolving in water can be found on YouTube.

**Self-sculpting of a dissolvable body due to gravitational convection,**

M. S. Davies Wykes, J. Huang, G. A. Hajjar, and L. Ristroph, *Physical Review Fluids* v. 3, pp. 043801 (2018). Journal

**Guiding microscale swimmers using teardrop-shaped posts,**

M. S. Davies Wykes, X. Zhong, J. Tong, T. Adachi, Y. Liu, L. Ristroph, M. D. Ward, M. J. Shelley, and J. Zhang, *Soft Matter* v. 13, pp. 4681–4688 (2017). Journal arXiv

**Dynamic self-assembly of microscale rotors and swimmers,**

M. S. Davies Wykes, J. Palacci, T. Adachi, L. Ristroph, X. Zhong, M. D. Ward, J. Zhang, M. J. Shelley, *Soft Matter* v. 12, pp. 4584–4589 (2016). Journal arXiv

**On the meaning of mixing efficiency for buoyancy-driven mixing in stratified turbulent flows,**

M. S. Davies Wykes, G. Hughes and S. B. Dalziel, *Journal of Fluid Mechanics* v. 781, pp. 261–275 (2015). Journal PDF

**Efficient mixing in stratified flows: experimental study of a Rayleigh-Taylor unstable interface within an otherwise stable stratification,**

M. S. Davies Wykes and S. B. Dalziel, *Journal of Fluid Mechanics* v. 756, pp. 1027-1057 (2014). Journal PDF

**Energetics of mixing for the filling box and the emptying-filling box,**

M. S. Davies Wykes, C. Hogg, J. Partridge and G. O. Hughes, (In preparation). arXiv

**Efficient mixing in stratified flows: Rayleigh-Taylor instability within an otherwise stable stratification,**

PhD thesis (2014). PDF

**Stability of a Rotating Boundary Layer,**

Master's thesis (2010). PDF

**Thin casting of silicon,**

For Elkem and Teknova, 91st European Study Group with Industry Bristol (2013).

**Train positioning and track location using video odometry and track curvature,**

For RDS International, 100th European Study Group with Industry Oxford (2014).