Turbulence—the chaotic motion of fluids—governs how energy and momentum move through the atmosphere and oceans, shaping jets, storm tracks and mixing, and therefore affecting climate and extreme events. Because models cannot resolve all turbulent scales, they rely on closures built largely on idealised three dimensional turbulence, where energy cascades downscale. Real geophysical flows, however, are rotating, stratified and often confined in thin layers. Under these conditions, turbulence can split its energy simultaneously upscale and downscale (a bidirectional cascade), with a sharp onset as control parameters (e.g. rotation or aspect ratio) change. There is no quantitative theory for when this transition occurs, how the energy split depends on parameters, or which mechanisms drive it. This limits our ability to represent mixing, dissipation and the emergence of large scale structures in environmental models.
This project set out to: (i) identify mechanisms responsible for the onset of bidirectional cascades; (ii) characterise their spatial and spectral signatures across scales; and (iii) develop a simple, quantitative model for the bidirectional cascade that can inform improved closures. Two complementary lenses were combined:
- Spatial perspective: track how structures stretch, split, thin or merge across scales, to quantify their contributions to forward (downscale) and inverse (upscale) transfer.
- Spectral perspective: analyse how interactions among Fourier modes depend on their phases; sustained flux requires phase organisation (“synchronisation”) across triads of interacting modes.
High performance simulations (reduced “shell” models, two dimensional turbulence, and a large wall bounded flow used for a deviation study) enabled unprecedented sampling of noisy, nonlocal triad interactions, and provided the data needed to test theory. The key novelty is elevating triad phase dynamics from anecdotal evidence in extreme events to a predictive, scale by scale framework that links directly to energy flux.
Pathway to impact: (a) open diagnostics and datasets to detect and quantify the balance between inverse and forward transfer; (b) theory informed parameterisations of energy flux direction and magnitude for weather, ocean and climate models; (c) practical guidance on when inverse cascade effects are expected and how to adjust closures; and (d) open source tools that lower the barrier to analysing cascade physics.
