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

Turbulence at very large scales is a complex, nonlinear problem of fundamental scientific and
societal 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 flows
of paramount industrial and geophysical importance requires a subgrid which covers a greater
range of scales - and hence must encode more of the turbulent dynamics. There is, therefore, a
pressing need for answers to long-standing questions on the dynamics of energy transfer
mechanisms in strongly turbulent fluids. This proposal is focused on establishing this new
understanding, focusing on both the dynamical processes at play in the turbulent energy cascade
and the rare, small-scale intermittent bursting events which are associated with extreme local
values of drag or heat transfer. The new methodology is rooted in dynamical systems theory built
around exact, unstable solutions of the governing equations. This approach has been
transformative in transitional/weakly turbulent flows, but has so far proved challenging to apply in
parameter regimes of industrial relevance, due to the difficulties associated with identifying and
converging the unstable solutions. These limitations are overcome here via a new approach using
novel machine learning algorithms and differentiable programming - with the necessary compute
power 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 Koopman
operator, which will be used both as both a tool to understand the dynamics encapsulated in the
unstable solutions (and around them in phase space) and also to probe even more strongly
turbulent flows to establish the dominant mechanisms and assess exactly which dynamical
processes are required in the subgrid scale models of the future.