Intermittency

In Figure 2.5 are shown the probability density functions of vorticity fluctuations $\delta_r \omega$ at various $r$, rescaled by their rms value $\langle (\delta_r \omega)^2 \rangle^{1/2}$.

As the separation decreases, the probability of observing very weak or very intense vorticity excursions increases at the expense of fluctuations of average intensity. This phenomenon goes under the name of intermittency. The non-similarity of the probability density functions reflects in the non-linear behavior for the scaling exponents predicted by Eq. (2.33).

Figure: Probability density functions of normalized vorticity increments $\delta_r \omega/\langle (\delta_r \omega)^2\rangle^{1/2}$. Here, $r=0.20$ ($+$), $r=0.07$ ($\times$), $r=0.02$ ( $\bigtriangledown$). For large separations the statistics is close to Gaussian, becoming increasingly intermittent for smaller $r$.