Paul Pruzina

Paul Pruzina


I completed my Masters in Mathematics  (Part III) at the University of Cambridge in 2019, including an extended essay project on the Madden-Julian Oscillation. I began my PhD at the University of Leeds in October 2019.

Research interests

My PhD concerns the formation of staircase structures in fluid dynamical systems, and is funded by the NERC Panorama DTP.

Stratified turbulent fluids display a range of complex behaviours, and one of the most striking is the spontaneous development of density staircases, consisting of well-mixed layers of nearly constant density, separated by sharp interfaces with high density gradients.  These staircases are present in some regions of the oceans with overall stable salinity gradients, and can be induced in lab experiments through suitable stirring of a fluid with a stable salt gradient. They also appear as a result of double diffusive convection, both in the oceans, and the astrophysical context of stellar interiors. A variety of explanations have been suggested for why staircases form, and progress has been made both experimentally and through numerical simulations, but there is no consensus on exactly why and how they develop.

My research is based on theory by Phillips (1972) who suggested that staircases form as a result of negative turbulent diffusion of density. This can be modelled by a diffusion equation for the density, where the density flux depends non-monotonically on the density gradient. Further work by Balmforth et al. (1998) extended this into a working model for layering in a stratified fluid forced by stirring. I have worked on extending this by adding diffusive effects, so that it can be used to make predictions for different fluids in specific conditions. As well as this, I have developed a similar model for layering in double diffusive convection. This style of model has potential to be applied to a range of layered systems, such as atmospheric potential vorticity staircases, and ExB staircases in plasmas.

Potential for High Impact Outcomes

Turbulent fluxes through staircases are significantly higher than in surrounding the surrounding fluid, so to accurately model (e.g.) heat or salt transport, it is essential to have a good understanding of staircase formation and evolution. With large areas of oceans susceptible to double diffusive layering, this makes modelling staircases important for parameterising ocean-air / ocean-ice heat flux, which is key in climate modelling.


  • BA and MMath Mathematics, University of Cambridge

Research groups and institutes

  • Astrophysical and Geophysical Fluid Dynamics