Directed percolation (DP) has recently emerged as a possible solution to the century old puzzle surrounding the transition to turbulence. Multiple model studies reported DP exponents, however, experimental evidence is limited since the largest possible observation times are orders of magnitude shorter than the flows’ characteristic timescales. An exception is cylindrical Couette flow where the limit is not temporal, but rather the realizable system size. We present experiments in a Couette setup of unprecedented azimuthal and axial aspect ratios. Approaching the critical point to within less than 0.1% we determine five critical exponents, all of which are in excellent agreement with the 2+1D DP universality class. The complex dynamics encountered at the onset of turbulence can hence be fully rationalized within the framework of statistical mechanics.
Physical Review Letters
We thank T.Menner, T.Asenov, P. Maier and the Miba machine shop of IST Austria for their valuable support in all technical aspects. We thank Marc Avila for comments on the manuscript. This work was supported by a grant from the Simons Foundation (662960, B.H.). We acknowledge the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement 306589 for financial support. K.A. acknowledges funding from the Central Research Development Fund of the University of Bremen, grant number ZF04B /2019/FB04 Avila Kerstin (”Independent Project for Postdocs”). L.K. was supported by the European Union’s Horizon 2020 Research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 754411.
Klotz L, Lemoult GM, Avila K, Hof B. Phase transition to turbulence in spatially extended shear flows. Physical Review Letters. 2022;128(1). doi:10.1103/PhysRevLett.128.014502
Klotz, L., Lemoult, G. M., Avila, K., & Hof, B. (2022). Phase transition to turbulence in spatially extended shear flows. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.128.014502
Klotz, Lukasz, Grégoire M Lemoult, Kerstin Avila, and Björn Hof. “Phase Transition to Turbulence in Spatially Extended Shear Flows.” Physical Review Letters. American Physical Society, 2022. https://doi.org/10.1103/PhysRevLett.128.014502.
L. Klotz, G. M. Lemoult, K. Avila, and B. Hof, “Phase transition to turbulence in spatially extended shear flows,” Physical Review Letters, vol. 128, no. 1. American Physical Society, 2022.
Klotz L, Lemoult GM, Avila K, Hof B. 2022. Phase transition to turbulence in spatially extended shear flows. Physical Review Letters. 128(1), 014502.
Klotz, Lukasz, et al. “Phase Transition to Turbulence in Spatially Extended Shear Flows.” Physical Review Letters, vol. 128, no. 1, 014502, American Physical Society, 2022, doi:10.1103/PhysRevLett.128.014502.