---
slug: paper-de-wit-x-m-et-al-2024-pattern-formation-by-turbulent-cascades
title: de Wit et al. (2024): Pattern Formation by Turbulent Cascades
canonical: https://miscsubjects.com/a/paper-de-wit-x-m-et-al-2024-pattern-formation-by-turbulent-cascades
---

## What the work establishes

X.M. de Wit and colleagues published 'Pattern formation by turbulent cascades' in Nature in 2024. The paper demonstrates that fully developed turbulence, usually viewed as structureless chaos, can produce ordered patterns through a fully nonlinear process. Energy from turbulent cascades piles up at an intermediate scale when both forward and inverse cascades arrest non-dissipatively. This selects a characteristic wavelength independent of system size or dissipation scales.

The core mechanism relies on odd viscosity in chiral fluids. Odd viscosity acts like a scale-dependent Coriolis force. It two-dimensionalizes flow at small scales, reversing the usual cascade directions compared to rotating fluids. Simulations and theory show spectral condensation at a tunable scale set by this coefficient.

## Exact primary work and passages

The primary source is de Wit, X.M., Fruchart, M., Khain, T. et al. Pattern formation by turbulent cascades. Nature 627, 515–521 (2024). https://doi.org/10.1038/s41586-024-07074-z

Key passage from the abstract: 'Here we show how to harness these seemingly structureless turbulent cascades to generate patterns. Pattern formation entails a process of wavelength selection, which can usually be traced to the linear instability of a homogeneous state. By contrast, the mechanism we propose here is fully nonlinear. It is triggered by the non-dissipative arrest of turbulent cascades: energy piles up at an intermediate scale, which is neither the system size nor the smallest scales at which energy is usually dissipated.'

Another passage: 'Using a combination of theory and large-scale simulations, we show that the tunable wavelength of these cascade-induced patterns can be set by a non-dissipative transport coefficient called odd viscosity, ubiquitous in chiral fluids ranging from bioactive to quantum systems.'

From the main text: 'We start with the almost paradoxical question of whether turbulence can be harnessed to generate patterns. ... energy is transferred to an intermediate length scale kc−1 ... structures emerge with characteristic size kc−1.'

## Convergence patterns evidenced

The work evidences several GRAIN convergence patterns. Energy flows in dissipative systems produce scale-invariant cascades that condense into structures with specific wavelengths. This matches branching and flow networks through vortex dynamics, waves via inertial and odd waves that decorrelate triads, symmetry breaking in chiral fluids, and bounded chaos in turbulence itself. Scale invariance appears in the universal spectra away from injection and dissipation scales. The mechanism operates across scales from fluids to potential atmospheric and plasma contexts.

## Distance from the full OIP/GRAIN synthesis

The paper sits at moderate distance from the full synthesis. It rigorously shows how difference in energy injection leads to flow cascades that produce structure via nonlinear arrest and memory-like spectral condensation. It does not address the later rungs of the Ladder from structure to memory to life to mind. The reader remains external; no Mirror Layer is invoked. The results supply a concrete physical instance of grain-like pattern emergence from flows but stay within fluid dynamics.

## Honest limits and disconfirming edges

The evidence rests on theory plus large-scale simulations in idealized chiral fluids. No direct laboratory experiments on odd-viscosity turbulence appear in the reported work. The mechanism requires specific conditions: non-dissipative arrest and combined direct-inverse cascades. It does not claim to explain all pattern formation; linear instabilities remain the standard route in many systems. Reductionist objections apply directly: the patterns are scale-selected by transport coefficients, not by any deeper teleology. Extension to natural systems such as solar wind or droplet coagulation remains speculative discussion without quantitative matching.

## Relation to OIP loop

The OIP loop maps cleanly onto the reported physics. The work object is the turbulent flow field. Invocation occurs through energy injection at chosen scales. The ledger records the energy spectrum E(k) and cascade directions. Receipts appear as the emergent patterns at kc−1 with verifiable wavelength. Replay follows by varying odd viscosity or rotation rate. Repair occurs when dissipation or boundaries alter the pile-up.

The synthesis receives concrete support at the flow-to-structure transition. Energy flows reliably select narrow families of patterns through the described nonlinear route. Limits remain explicit: the work stops at structure and does not reach memory or mind.
