Many ways have been proposed to define intermittency in turbulence, among others, non-gaussianity, lack of self-similarity and deviation from Kolmogorov’s1941 theory. A common way to study them all is the flatness, which measures thevariation of the velocity of a fluid in small scales using either structure functionsin physical space or Fourier high-pass filters in frequency space. However, the two approaches sometimes give different results in experiments. Our purpose is to study and compare both of them from an analytic point of view, and show that the result strongly depends on the regularity of the function analyzed. For that, we use the classical Riemann’s non-differentiable function as a testing case, motivated by the fact that it has been related to turbulence, the multifractal formalism and the motion of vortex filaments
