Anomalous dissipation is considered one of the defining features of turbulence. Energy dissipates at a rate independent of viscosity — turn the viscosity dial, and the dissipation rate stays the same. This has been observed experimentally, predicted theoretically, and enshrined as fundamental. Kankaria, Mukherjee, Murugan, Rosti, and Ray show that it depends on which triadic interactions you keep.
Triadic interactions are the elementary unit of nonlinearity in the Navier-Stokes equations — three Fourier modes coupling together to transfer energy. In full turbulence, all possible triads participate. The authors systematically remove subsets of triads and measure what happens. When certain classes of interactions are suppressed, anomalous dissipation vanishes. The energy dissipation becomes viscosity-dependent again. Normal behavior returns.
This means anomalous dissipation is not a generic consequence of the Navier-Stokes equations. It's a specific consequence of the full combinatorial richness of the nonlinear term. Simplify the nonlinearity — remove certain triads — and the defining pathology of turbulence disappears.
The implication is philosophical as much as physical. Anomalous dissipation was treated as an inevitable feature of any sufficiently complex fluid flow. It's actually a fragile feature that requires the complete interaction network. Turbulence is not a robust phenomenon — it's a contingent one, dependent on the full combinatorial structure of its nonlinearity. Remove the right pieces and the monster becomes tame.