Isotropic turbulence: Important differences between true dissipation rate and its one-dimensional surrogate

The one-dimensional surrogate (1D) of energy dissipation rate has often been used in place of the true one in investigations of the Kolmogorov refined similarity hypothesis and the multifractal nature of isotropic turbulence. Direct numerical simulations, reported here, show that the use of the 1D surrogate can lead to fundamental changes in statistics. The conditional and unconditional probability densities of the Kolmogorov variable built from the true dissipation are never bimodal and always nearly Gaussian.