Can Kolmogorov-Scale Fibers Measure the Mean Turbulent Dissipation?

In turbulent flows, characterizing the structure and dynamics of small-scale motions requires accurate knowledge of the nine components of the velocity gradient tensor, A_ij =∂u_i /∂x_j (i,j =1,2,3). This information enables the derivation of tensorial and scalar quantities that describe the local topological features of turbulence, as well as universal mechanisms governing its dynamics. Among the most relevant information derived from A_ij, the mean rate 〈ε〉 at which viscosity converts the kinetic energy of turbulent fluctuations into heat remains undisputedly a fundamental quantity for both practical applications and theoretical formulations. Despite recent advances in optical measurement techniques, experimental evaluations of 〈ε〉 strictly relying on its formal definition have so far proven challenging, as the direct and complete evaluation of A_ij generally requires three‑dimensional velocity field acquisitions with spatial resolution on the order of the Kolmogorov length scale, η. In this context, optical tracking of rigid anisotropic particles (e.g., fibers and rods), which are known to carry statistical signatures of the velocity gradient tensor, offers a promising alternative for probing small‑scale eddying motions and directly measuring the dissipation rate in turbulent flows. In this study, fiber-laden direct numerical simulations using a point-wise fiber model and experiments are performed in turbulent channel flow at three shear Reynolds numbers (Re_τ = 180, 360, 720). Considering fibers with small inertia and lengths between 1.5η and 13η, this investigation provides the first direct measurement of 〈ε〉 through the fiber mean-square angular velocity 〈ω_p²〉. Specifically, the results indicate that, across most of the channel height—where the effects of mean shear and fiber preferential orientation are small—〈ω_p²〉 estimates the mean dissipation rate with an average relative error of approximately 8.2%.