- Open Access
Angular Velocity of Kolmogorov-Scale Fibers as Proxy for Turbulent Dissipation
Phys. Rev. Lett. 136, 054001 – Published 3 February, 2026
DOI: https://doi.org/10.1103/kcmw-5dph
Abstract
We introduce a fiber-based method to directly measure turbulent energy dissipation. Combining original measurements of the full-body rotation—tumbling and spinning—of short, Kolmogorov-scale fibers in turbulent channel flow with direct numerical simulations using a point-fiber model, we show that the mean-square angular velocity closely reproduces the mean dissipation rate. The method is accurate both in the nearly homogeneous turbulence of the channel center and in the logarithmic layer, with a mean deviation below 6%, demonstrating that Kolmogorov-scale fibers provide a robust and reliable tool for quantifying dissipation.
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References (43)
- M. Schröder, T. Bätge, E. Bodenschatz, M. Wilczek, and G. Bagheri, Estimating the turbulent kinetic energy dissipation rate from one-dimensional velocity measurements in time, Atmos. Meas. Tech. 17, 627 (2024).
- B. R. Pearson, P.-A. Krogstad, and W. van de Water, Measurements of the turbulent energy dissipation rate, Phys. Fluids 14, 1288 (2002).
- G. Wang, F. Yang, K. Wu, Y. Ma, C. Peng, T. Liu, and L.-P. Wang, Estimation of the dissipation rate of turbulent kinetic energy: A review, Chem. Eng. Sci. 229, 116133 (2021).
- J. C. Vassilicos, Dissipation in turbulent flows, Annu. Rev. Fluid Mech. 47, 95 (2015).
- A. N. Kolmogorov, On the degeneration of isotropic turbulence in an incompressible viscous fluid, Dokl. Akad. Nauk SSSR 31, 538 (1941).
- A. N. Kolmogorov, The local structure of turbulence in incompressible viscous fluids for very large Reynolds numbers, Dokl. Akad. Nauk SSSR 30, 299 (1941); reprinted in Proc. R. Soc. A 434, 9 (1991).
- A. N. Kolmogorov, Dissipation of energy in isotropic turbulence, Dokl. Akad. Nauk SSSR 32, 19 (1941).
- S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, England, 2000).
- S. Brizzolara, M. E. Rosti, S. Olivieri, L. Brandt, M. Holzner, and A. Mazzino, Fiber tracking velocimetry for two-point statistics of turbulence, Phys. Rev. X 11, 031060 (2021).
- B. W. Zeff, D. D. Lanterman, R. McAllister, R. Roy, E. J. Kostelich, and D. P. Lathrop, Measuring intense rotation and dissipation in turbulent flows, Nature (London) 421, 146 (2003).
- J. A. Mullin and W. J. A. Dahm, Dual-plane stereo particle image velocimetry measurements of velocity gradient tensor fields in turbulent shear flow. I. Accuracy assessments, Phys. Fluids 18, 035101 (2006).
- T. B. Oehmke, A. D. Bordoloi, E. Variano, and G. Verhille, Spinning and tumbling of long fibers in isotropic turbulence, Phys. Rev. Fluids 6, 044610 (2021).
- V. Giurgiu, G. C. A. Caridi, M. De Paoli, and A. Soldati, Full rotational dynamics of plastic microfibers in turbulence, Phys. Rev. Lett. 133, 054101 (2024).
- S. Parsa, E. Calzavarini, F. Toschi, and G. A. Voth, Rotation rate of rods in turbulent fluid flow, Phys. Rev. Lett. 109, 134501 (2012).
- S. Parsa and G. A. Voth, Inertial range scaling in rotations of long rods in turbulence, Phys. Rev. Lett. 112, 024501 (2014).
- S. Bounoua, G. Bouchet, and G. Verhille, Tumbling of inertial fibers in turbulence, Phys. Rev. Lett. 121, 124502 (2018).
- N. Pujara, J.-A. Arguedas-Leiva, C. C. Lalescu, B. Bramas, and M. Wilczek, Shape- and scale-dependent coupling between spheroids and velocity gradients in turbulence, J. Fluid Mech. 922, R6 (2021).
- L. J. Baker and F. Coletti, Experimental investigation of inertial fibres and disks in a turbulent boundary layer, J. Fluid Mech. 943, A27 (2022).
- G. B. Jeffery, The motion of ellipsoidal particles immersed in a viscous fluid, Proc. R. Soc. A 102, 161 (1922).
- R. Betchov, An inequality concerning the production of vorticity in isotropic turbulence, J. Fluid Mech. 1, 497 (1956).
- P. L. Johnson and M. Wilczek, Multiscale velocity gradients in turbulence, Annu. Rev. Fluid Mech. 56, 463 (2024).
- D. A. Donzis and K. R. Sreenivasan, The bottleneck effect and the Kolmogorov constant in isotropic turbulence, J. Fluid Mech. 657, 171 (2010).
- J. Jiménez, Near-wall turbulence, Phys. Fluids 25, 101302 (2013).
- V. Giurgiu, G. C. A. Caridi, M. Alipour, M. De Paoli, and A. Soldati, The TU Wien Turbulent Water Channel: Flow control loop and three-dimensional reconstruction of anisotropic particle dynamics, Rev. Sci. Instrum. 94, 095101 (2023).
- G. A. Voth and A. Soldati, Anisotropic particles in turbulence, Annu. Rev. Fluid Mech. 49, 249 (2017).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/kcmw-5dph for additional details about (i) experimental data processing, which includes Refs. [13,27,28]; (ii) point-fiber direct numerical simulations, which includes Refs. [17,19,21,25,29–37]; and (iii) the filtered velocity gradient, which includes Refs. [17,30,38].
- M. Alipour, Orientation and rotation rates of non-axisymmetric fibers in turbulent channel flow, Ph.D. thesis, Wien, 2021.
- G. C. A. Caridi, V. Giurgiu, M. De Paoli, and A. Soldati, Complete solid-body rotation rate measurements of micro-plastic curved fibers in turbulence, Exp. Fluids 66, 102 (2025).
- J. Kim, P. Moin, and R. Moser, Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech. 177, 133 (1987).
- C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics (Springer, Berlin, Heidelberg, 1988).
- H. Zhang, G. Ahmadi, F.-G. Fan, and J. B. McLaughlin, Ellipsoidal particles transport and deposition in turbulent channel flows, Int. J. Multiphase Flow 27, 971 (2001).
- P. H. Mortensen, H. I. Andersson, J. J. J. Gillissen, and B. J. Boersma, Dynamics of prolate ellipsoidal particles in a turbulent channel flow, Phys. Fluids 20, 093302 (2008).
- C. Marchioli, M. Fantoni, and A. Soldati, Orientation, distribution, and deposition of elongated, inertial fibers in turbulent channel flow, Phys. Fluids 22, 033301 (2010).
- C. Marchioli and A. Soldati, Rotation statistics of fibers in wall shear turbulence, Acta Mech. 224, 2311 (2013).
- C. Marchioli, L. Zhao, and H. I. Andersson, On the relative rotational motion between rigid fibers and fluid in turbulent channel flow, Phys. Fluids 28, 013301 (2016).
- H. Brenner, The Stokes resistance of an arbitrary particle—IV Arbitrary fields of flow, Chem. Eng. Sci. 19, 703 (1964).
- M. Shapiro and M. Goldenberg, Deposition of glass fiber particles from turbulent air flow in a pipe, J. Aerosol Sci. 24, 65 (1993).
- C. C. Lalescu and M. Wilczek, Acceleration statistics of tracer particles in filtered turbulent fields, J. Fluid Mech. 847, R2 (2018).
- A. Pumir, H. Xu, and E. D. Siggia, Small-scale anisotropy in turbulent boundary layers, J. Fluid Mech. 804, 5 (2016).
- R. Ni, N. T. Ouellette, and G. A. Voth, Alignment of vorticity and rods with Lagrangian fluid stretching in turbulence, J. Fluid Mech. 743, R3 (2014).
- T. J. DiCiccio and B. Efron, Bootstrap confidence intervals, Stat. Sci. 11, 189 (1996).
- L. Zhao and H. I. Andersson, Why spheroids orient preferentially in near-wall turbulence, J. Fluid Mech. 807, 221 (2016).
- D. Zaza, V. Giurgiu, M. Iovieno, and A. Soldati, Data for: Angular velocity of Kolmogorov-scale fibers as proxy for turbulent dissipation, 10.5281/zenodo.17873151 (2026), data set.