Dynamical arrest in active nematic turbulence

Active fluids display spontaneous turbulent-like flows known as active turbulence. Recent work revealed that these flows have universal features, independent of the material properties and of the presence of topological defects. However, the differences between defect-laden and defect-free active turbulence remain largely unexplored. Here, by means of large-scale numerical simulations, we show that defect-free active nematic turbulence can undergo dynamical arrest. This state is characterized by an emergent network of nematic domain walls that channels coherent streams and suppresses chaotic flows. As the system evolves, the branched wall network produces a large-scale pattern with tree-like topological properties. We find that flow alignment – the tendency of nematics to reorient under shear – enhances large-scale chaotic jets in contractile rodlike systems while promoting dynamical arrest in extensile systems. We further show that dynamical arrest persists regardless of whether defects are prohibited by construction or simply fail to form due to a high energy cost of defect cores. Taken together, our findings reveal a striking pattern-formation mechanism, with labyrinths emerging from active turbulence, and illuminate the rich transitional regime between defect-free and defect-laden dynamics. These behaviors call for the experimental realization of active nematics at vanishing or low defect densities, and underscore that, in extensile rodlike nematics, topological defects enable turbulence by preventing dynamical arrest.

💡 Research Summary

In this work the authors investigate how the presence or absence of topological defects influences the turbulent dynamics of active nematic fluids. They extend a previously studied minimal director‑based model by incorporating flow‑alignment (parameter ν) and Ericksen stresses, thereby arriving at the active Ericksen‑Leslie formulation. The governing equations are expressed in terms of a stream function ψ and the nematic angle θ, with three key dimensionless groups: the activity number A (system size versus active length), the viscosity ratio R, and the flow‑alignment parameter ν. Simulations are performed on a periodic square domain at low Reynolds number, with A = 3 × 10⁵, R = 1, and various ν values, while the sign of the active stress S distinguishes extensile (S = +1) from contractile (S = −1) systems.

Two distinct regimes emerge depending on the product S ν. When S ν > 1 (contractile, flow‑aligning rods), the system exhibits strong, multiscale chaotic flows reminiscent of classic active turbulence. Large‑scale jets dominate the velocity spectrum, which displays a robust q⁻¹ scaling over a wide range of wavenumbers. Nematic domain walls appear, split, and dissolve continuously; the Frank‑energy spectrum is broad, indicating a distribution of wall separations. Correlation times for both velocity and nematic fields are short, confirming a highly dynamic state.

In contrast, for S ν < −1 (extensile, flow‑aligning rods) the dynamics change dramatically. Although small‑scale chaotic activity persists, large‑scale flows are strongly suppressed. Nematic distortions organize into a connected network of domain walls that spans the entire system. These walls act as channels for localized streams, and the velocity power spectrum shows a narrow peak at a characteristic wavelength rather than a broad inertial range. The wall network adopts a tree‑like topology: branches grow, bifurcate, and become “grid‑locked” when they encounter pre‑existing branches. This results in a state the authors term “dynamical arrest,” characterized by markedly longer correlation times, especially for the nematic tensor at large scales, and by slow, glass‑like ageing dynamics.

The authors explain the arrest mechanism as follows. The spontaneous‑flow instability inherent to active nematics generates shear that concentrates anti‑parallel flows along nematic walls. In the extensile, flow‑aligning case, these flows stabilize the walls, preventing their breakup. Wall growth proceeds via a zig‑zag instability that creates branches of decreasing size until a selected wavelength is reached. When a branch tip meets another wall perpendicularly, it is deflected and eventually blocked, leading to a frozen, space‑filling network. The walls host “pseudo‑defects,” localized topological structures that mimic true defects but arise solely from the director field’s continuous nature.

To test the robustness of this phenomenon, the authors also simulate the full Q‑tensor model, where the defect core size can be tuned. By increasing the core energy, defect nucleation is suppressed, reproducing the defect‑free arrest state. Lowering the core energy allows defects to proliferate sharply at a threshold, destroying the wall network and restoring conventional active turbulence. This transition underscores that topological defects act as catalysts for turbulence: their presence prevents dynamical arrest, while their absence permits the emergence of labyrinthine, arrested patterns.

The paper concludes that (i) the sign and magnitude of the flow‑alignment parameter ν, together with the activity sign S, dictate whether an extensile or contractile active nematic will display chaotic turbulence or dynamical arrest; (ii) even in the absence of true topological defects, active nematics can self‑organize into complex, tree‑like domain‑wall networks; and (iii) defect nucleation provides a control knob to switch between arrested and turbulent regimes. The authors suggest experimental verification in microtubule‑motor assays where defect density can be reduced (e.g., by increasing filament rigidity or by tuning motor activity) to observe the predicted labyrinthine arrest. Their findings broaden the understanding of pattern formation in active matter and reveal a rich transitional landscape between defect‑free and defect‑laden dynamics.