MLTURB: A new understanding of turbulence via a machine-learnt dynamical systems theory

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Turbulence at very large scales is a complex, nonlinear problem of fundamental scientific andsocietal importance. Turbulent computations often rely on a "subgrid" model for the smaller,dissipative scales of motion. However, accurate simulation and prediction in the large-scale flowsof paramount industrial and geophysical importance requires a subgrid which covers a greaterrange of scales - and hence must encode more of the turbulent dynamics. There is, therefore, apressing need for answers to long-standing questions on the dynamics of energy transfermechanisms in strongly turbulent fluids. This proposal is focused on establishing this newunderstanding, focusing on both the dynamical processes at play in the turbulent energy cascadeand the rare, small-scale intermittent bursting events which are associated with extreme localvalues of drag or heat transfer. The new methodology is rooted in dynamical systems theory builtaround exact, unstable solutions of the governing equations. This approach has beentransformative in transitional/weakly turbulent flows, but has so far proved challenging to apply inparameter regimes of industrial relevance, due to the difficulties associated with identifying andconverging the unstable solutions. These limitations are overcome here via a new approach usingnovel machine learning algorithms and differentiable programming - with the necessary computepower and expertise provided through a collaboration with Google's Accelerated Sciences team.These tools are complemented by a robust low-order modelling framework based on the Koopmanoperator, which will be used both as both a tool to understand the dynamics encapsulated in theunstable solutions (and around them in phase space) and also to probe even more stronglyturbulent flows to establish the dominant mechanisms and assess exactly which dynamicalprocesses are required in the subgrid scale models of the future.