Everyone knows that warm air rises and cold air sinks. Yet the implications of this apparently simple phenomenon are neither widely appreciated nor properly understood. The phenomenon produces vertical variations in temperature, known as thermal stratifications, that play a profound role in civil and environmental engineering. Thermal stratifications determine how much thermal and mechanical energy is needed to produce comfortable temperatures in the lowest parts of a room. By restricting the direction of air flow, thermal stratifications also determine the eventual fate of airborne pathogens and are therefore crucial in influencing the spread of viruses such as SARS-CoV-2 inside buildings. In reservoir management, thermal stratification is often biologically undesirable; hence energy is used for mixing to destratify the water. In water tanks, on the other hand, thermal stratifications are used as an effective means of storing solar-thermal energy. In all cases, the evaluation of appropriate design and control strategies requires understanding of how hot fluid and cold fluid interact to produce or destroy a stratification, which is an extremely challenging and open question at the forefront of current research in turbulence.

Summary

This project will address the outstanding problem of predicting the thermal stratifications that are produced by non-uniform heating and cooling of a confined space and culminate in a design tool called [D*]stratify, which will enable the prediction and control of stratifications by identifying and using a limited number of key measurements. Our approach will transcend existing models by discovering and accounting for the energy behind turbulent plumes and thermal stratifications, coupling theory with real-time measurements. Utilising existing infrastructure, we will initiate a unique working laboratory for producing thermal stratifications, alongside direct numerical simulations of confined turbulent plumes. Our discoveries and modelling will facilitate the prediction, design and manipulation of thermal stratifications for both research and operation, whilst providing fundamental information about the underlying energy conversions.

Probability density

We're developing models that describe the state of a system as a probability density that evolves with time. Here's a simple example using a stochastic version of the Lorenz equations:
\[\begin{aligned}
\mathrm{d}X_{t} &= s(Y_{t}-X_{t})+\sigma_{xx} \mathrm{d}\eta_{t}, \\
\mathrm{d}Y_{t} &=X_{t}(r-Z_{t})-Y_{t}+\sigma_{yy} \mathrm{d}\zeta_{t}, \\
\mathrm{d}Z_{t} &=X_{t}Y_{t}-b Z_{t}+ \sigma_{zz}\mathrm{d}\xi_{t}.
\end{aligned}\]