Research Projects

Turbulent flow, a high-dimensional chaotic system, is crucial in physical, biological, and engineering systems. A key feature of turbulence is its small-scale intermittency –localised occurrences of extreme velocity gradients in the flow which are orders of magnitude higher than the mean value and therefore highly impactful. This significantly influences phenomena associated with the flow, from light/sound wave propagation to local quenching of combustion. However, such extreme events are largely unexplained and extremely difficult to predict or control. This project aims to develop a complete understanding of the spatial structure and temporal dynamics of extreme occurrences in turbulence and design a predictive model for accurately forecasting such events. To accomplish this goal, it is necessary to simulate high Reynolds number turbulent flows using direct numerical simulations (DNS), resolving all scales of motion without any modelling. We will conduct massively parallel computations for DNS of forced isotropic turbulent flows at spectral accuracy. First, we will study the large-scale organisation and underlying structure of the intense turbulence regions. Our previous work provides a technique of triple decomposition of the local velocity gradients. Applying this method in the DNS data, we will characterise the structures of intense shear, normal-strain and rigid-body-rotation rates individually, instead of the commonly studied vorticity-strainrate decomposition that potentially obscures our understanding of turbulence intermittency. Next, we will study the time-evolution of velocity gradients following the Lagrangian trajectories of fluid particles in a turbulent flow. Literature reveals that these timeseries are chaotic and multifractal, implying a dependence on their time-histories. We will therefore employ a time-delay embedding based method to segregate the “well-behaved” linear dynamics of different flow processes from their intermittent dynamics and identify a suitable precursor to the occurrence of extreme velocity gradients. This will lead to a modeling framework that together with artificial-intelligence/machine-learning (AI/ML) models, will encode delay-embedded latent dynamics of intermittent time series for predicting future extreme events. We aim to develop a robust, generalizable, physics-inspired ML model that can forecast extreme turbulence based on time history of recorded flow data. Overall, this work will offer a comprehensive understanding of extreme events in turbulence, potentially answering long-standing questions of the community and laying the foundation for a unified theory of turbulence. It will also provide an accurate predictive model to forecast extreme events in turbulence that may help in design/control of wide-ranging systems, from combustion to cloud/rain formation. The model can be further extended to predict extreme events in chaotic systems of weather, oceanic rogue waves, and social/financial networks.