Synthetic simulation of turbulent flow using resolvent analysis

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In turbulent flows, transport processes and average flow quantities of great practical relevance are dominated by coherent structures. In an effort to better understand their role, a sophisticated approach - Resolvent Analysis (RA) - has emerged in recent years. The power of RA is that it yields a set of spatial modes describing the most important flow structures directly from the equations of motion and from knowledge of the mean flow, without requiring expensive scale-resolving simulations or experiments. However, RA only describes the kinematics of fluid motion and lacks the power to explain how structures across different scales interact dynamically with each other.The overarching aim of this project is to develop a methodology that can "close" a RA-based model. The fundamental idea is to determine amplitude coefficients to "weigh" the contribution of different structures such as to balance dynamical behaviour, thus providing a space-time turbulent velocity field that has been generated synthetically, without simulation. From a computational standpoint, this can be achieved by solving an optimisation problem of rather small dimension, owing to the compressive power of RA. The potential of the approach is that it would enable obtaining detailed insight into the dynamics of complex flows more cheaply than with scale-resolving simulation. In turn, this would facilitate and accelerate flow analysis, parameter exploration and engineering design in a variety of applications. The specific objectives of this research are to develop new algorithms and computational tools to suit this paradigm and to demonstrate the method in a variety of three-dimensional fluid systems of practical interest, such as turbulent flows in pipes/channels and separated flows around bluff and streamlined bodies.