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Hannah Kreczak

Senior Analyst
The National Audit Office
PhD Project Title
Rates of mixing in models of fluid devices with discontinuities


I spent the first four years of my academic study at the University of Leeds studying an Integrated Masters in Mathematics. During my studies I developed an interest in applied mathematics, taking modules in subjects ranging from Special Relativity and Cosmology, to Fluid Dynamics and Quantum Mechanics. During my first year of study on the Fluid Dynamics CDT I had the opportunity to undertake an MSc project looking at the dynamics of downdraughts in the atmosphere with an accompanying placement at the Met Office. This was my first experience using large scale experiments to investigate and validate mathematical theory and computational fluid models.

Research Interests

My research interests lie in using techniques in modelling fluid flows as dynamical systems, specifically looking at mixing rates via chaotic advection. Through abstract models capturing the essence of fluid mixing, such as the stretching and folding of fluid elements, I am able to analytically and computational investigate how the rate of mixing changes depending on the stirring protocol and fluid properties. Currently I am investigating the effect of discontinuities on rates of mixing, which can arise in micro-mixing configurations and granular material. Via an ergodic theoretic deriving transfer operators acting on functional spaces of concentration fields, I compute typical finite time and asymptotic mixing rates with and without the inclusion of molecular diffusion.

In stirring fields which are predominantly chaotic and exponentially mixing, it is observed that the addition of discontinuous transformations can contaminate mixing when the stretching rates are uniform, or close to uniform. The contamination comes from an increase in scales of the concentration field by the reassembly of striations when cut and shuffled. A deceleration of mixing with increasing diffusion coefficient can be observed, sometimes overshooting analytically derived bounds in the diffusionless limit. Read my paper on Deceleration of one-dimensional mixing by discontinuous mappings.

Why I chose the CDT in Fluid Dynamics

I was recommended the CDT by my previous supervisor and chose to apply due to the range in projects that would be offered and the multi-disciplinary approach amongst the cohort and taught modules. I feel that the CDT offers excellent experience in applications of research in both academia and industry, and believe that the professional skills that I am developing will be transferable to many a career. Currently I am interested in pursuing a career in public engagement and outreach for STEM subjects.


Best Student Presentation prize Runner up - UK Fluids Conference 2017, Leeds, UK


Kreczak, R. Sturman, and M. C. T. Wilson,“Deceleration of one-dimensional mixing by discontinuous mappings,” Phys. Rev. E. 96, 053112 (2017).

Public Engagement Projects

Pint of Science Leeds (2016-2018) - helping establish the international science festival in Leeds. Roles as Team Leader and Treasurer.