Local equilibrium hypothesis and Taylor’s dissipation law

To qualitatively investigate the validity of Kolmogorov local equilibrium hypothesis and the Taylor dissipation law, we conduct direct numerical simulations of the three-dimensional turbulent Kolmogorov flow. Since strong scale-by-scale (i.e. Richardson-type) energy cascade events occur quasi-periodically, the kinetic energy of the turbulence and its dissipation rate evolve quasi-periodically too. In this unsteady turbulence driven by a steady force, instantaneous values of the dissipation rate obey the scaling recently discovered in wind tunnel experiments (Vassilicos 2015 Ann. Rev. Fluid Mech. 47 95–114) instead of the Taylor dissipation law. The Taylor dissipation law does not hold because the local equilibrium hypothesis does not hold in a relatively low wave-number range. The breakdown of this hypothesis is caused by the finite time needed for the energy at such large scales to reach the dissipative scale by the scale-by-scale energy cascade.