Turbulence is defined by its intermittency — extreme events that are far more frequent than Gaussian statistics would predict. These bursts of intense velocity gradients produce the anomalous dissipation that has resisted analytical understanding since Kolmogorov's 1941 theory. The energy cascade from large scales to small is the standard story. But what drives the intermittency?
Kankaria, Mukherjee, Murugan, Rosti, and Ray (arXiv: 2603.19180) answer by subtraction. They systematically thin the triadic interaction network in Fourier space — removing modes while preserving the equation's structure — and watch what happens. As modes are removed, intermittency fades. Structure-function exponents approach their dimensional (non-anomalous) values. The multifractal spectrum contracts. Dissipation rates vanish at high Reynolds numbers instead of remaining finite.
The through-claim: anomalous dissipation is not a generic property of the Navier-Stokes equations. It requires the full combinatorial richness of triadic interactions. A thinned set of modes, even a substantial one, produces turbulence that behaves classically — no intermittency, no anomalous scaling, no finite dissipation in the inviscid limit. The pathology that makes turbulence hard isn't in the nonlinearity per se; it's in the density of the nonlinear coupling network.
This reframes the turbulence problem. The question isn't “why is turbulence intermittent?” but “what is the minimum interaction density needed to sustain intermittency?” Turbulence isn't inherently wild. It becomes wild only when enough modes talk to enough other modes. Prune the conversation and the wildness disappears.
Kankaria, Mukherjee, Murugan, Rosti & Ray, 2603.19180. Turbulence / intermittency / anomalous dissipation / triadic interactions.