  In the study of turbulence, intermittency is a measure of how much
Kolmogorov's theory of 1941 deviates from experiments. It is quantified with
the flatness of the velocity of the fluid, usually based on structure functions
in the physical space. However, it can also be defined with Fourier high-pass
filters. Experimental and numerical simulations suggest that the two approaches
do not always give the same results. Our purpose is to compare them from the
analytical point of view of functions. We do that by studying generalizations
of Riemann's non-differentiable function, yielding computations that are
related to some classical problems in Fourier analysis. The conclusion is that
the result strongly depends on regularity. To visualize this, we establish an
analogy between these generalizations and the influence of viscosity in
turbulent flows. This article is motivated by the mathematical works on the
multifractal formalism and the discovery of Riemann's non-differentiable
function as a trajectory of polygonal vortex filaments.
