Noise in convection: modelling and analysis

• Applicant: Dr. Theresa Lange
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 569224218

In the last decades, noise has become a valuable tool in studying the dynamics of fluids: their complex behaviour is driven by the interplay of inherent large scale and small scale structures and stochastic modelling has proven to capture the highly oscillatory character of the later. Random perturbations of fluid models have attracted a lot of attention in recent years displaying a plethora of new phenomena such as regularisation and chaotic behaviour in contrast to the deterministic theory where the proofs of corresponding results are widely open. A particularly important field in fluid dynamics is convection (the theory of heat transport) where fluids are coupled to a temperature field, finding crucial applications in a variety of contexts, from industry and engineering to geophysical sciences to astrophysics. Key questions concern the modelling, the control of heat transfer, and corresponding patterns, such as periodic cells and aperiodic shapes. Though convection has been widely studied in the deterministic literature, the regimes of the onset of instabilities and ultimate turbulence still remain a huge challenge in that corresponding phenomena are hard to capture in experiments and existing theory can provide only approximate answers (if any) to the above questions. Thus, the goal of our project is to achieve a deep understanding of the role of randomness in the above convection problems. In this pursuit we will a) determine suitable stochastic representations capturing the fluctuations of convective flows so as to reproduce currently existing predictions in the turbulent case; b) study the regularizing effect of such random perturbations on the models as well as arising patterns; c) critically discuss our findings by exploring limitations of such stochastic models in terms of well-posedness.

• DFG Programme: Emmy Noether Independent Junior Research Groups