Inverting turbulence: flow patterns and parameters from sparse data

Our ability to compute turbulent flows with scale-resolving simulations, like Large Eddy and Direct Numerical simulations, has grown tremendously in the past decades. In these simulations, problem parameters and boundary conditions are specified and the forward problem is solved. In many real-life settings however, this information maybe uncertain or not available at all. For many of these turbulent flows observational data, such as velocity or scalar measurements, are available at several sensor locations. These sensors can be either static or mobile (for example wearable devices that monitor air quality are now cheap and easily affordable). The available observational data can be assimilated with the governing equations to recover the missing information. This is achieved by formulating and solving an optimisation problem that minimises the difference between the estimated and observed values at the sensor points. The solution to this problem provides the velocity and scalar fields that satisfy the equations and optimally match with the available observations. This is known as the inverse problem and in this sense turbulence is "inverted". Available methods to solve this optimisation problem however either fail or quickly become intractable for turbulent flows (due to the so called "butterfly effect"). We aim to break the impasse by formulating a new approach with affordable computational cost and apply it to an environmental problem, flow and pollutant dispersion around a building. Success in this endeavour can open a new direction of research, and can lead to entirely new technologies, as described in more detail in the case of support.