This PhD thesis, funded by the ANR RedLUM project, in collaboration with Inria Bordeaux, the Sant'Anna School of Advanced Studies, and the companies Scalian DS and Weather Measures, aims to develop an effective simulation framework for controlling agricultural frost using wind towers at the scale of an agricultural plot. The PhD student will work with the partners to design a reduced model to simulate the dynamics of turbulent flows at high Reynolds, which are often computationally expensive.

The aim is to reduce the dimensionality of the models by using techniques such as proper orthogonal decomposition (POD) and Galerkin's method to approximately simulate the complex dynamics of turbulent flows. However, these models suffer from insufficient representation of solution fields, making it difficult to accurately approximate dynamical systems. To overcome these challenges, stochastic closure-based approaches are used to model chaotic dynamics by stochastic differential equations. Predictions are then corrected in real time using a data assimilation process.

The PhD work involves the development and validation of these dimension reduction and data assimilation techniques for 3D incompressible turbulent flows, processing synthetic and experimental data. The project also includes the study of unknown turbulence conditions and the development of hyper-efficient reduction techniques to handle non-linear terms.