Fig. 5: Active turbulence.
From: Shaping active matter from crystalline solids to active turbulence
a Instantaneous motion of disks colored by their speed ∣U∣ and concentration field \(c/{c}_{\max }\). Here, Pe = 20, ϕ = 0.5, and the domain size is L = 200. b, vortex-showing streamlines and vorticity component ωE ⋅ ez of the continuum flow field UE. c Clusters characterized by the number Nclu of their constituting disks and the size lclu of the largest cluster. b, c showing the full domain are scaled versus a. d, probability density function (PDF) of the vortex size lvtx with a mean of \(\ell \)vtx ≈ 8. e History of lclu and its time-averaged value \(\ell \)clu ≈ 87. f, kymograph of \({\Phi }_{{{{{{{{\rm{E}}}}}}}}}{| }_{x=\frac{L}{2}}\) implies chaos and fading oscillatory patterns. g PDF of the disk' velocity component U. h, PDF of the longitudinal velocity difference \(\Delta {U}^{\parallel }({{{{{{{\mathcal{R}}}}}}}})\) between two disks separated by a distance \({{{{{{{\mathcal{R}}}}}}}}\) when Pe = 5. i Similar to (h) but for Pe = 20. In g–i, 〈s〉 and σs denote the average and standard deviation of a random variable s, respectively; the curve represents the unit-variance Gaussian function \(1/\sqrt{2\pi }\exp (-{s}^{2}/2)\). j Kinetic energy spectrum \(E(\hat{q})\) versus the modified wavenumber \(\hat{q}\) (SI Sec. I.E), with an additional dataset incorporated for an expanded domain where L = 400. Here, qc = π is the characteristic wavenumber corresponding to the disk diameter. The left vertical line indicates the size, \(\ell \)clu ≈ 87 of the largest cluster, while the right line marks the mean vortex size, \(\ell \)vtx ≈ 8; both pertain to the case of L = 200. See Source data.
