 Intermittency (turbulence)

Intermittency is the uneven concentration of turbulent fluctuations or dissipation into relatively intense events separated by quieter regions or intervals. It often appears statistically as increasingly non-Gaussian velocity or magnetic-field increments at smaller separations. A turbulent signal can therefore have a moderate average variance while rare events dominate its higher moments.^[ref]

One useful diagnostic is the increment flatnessusing the same structure function component and convention in both moments. A centered Gaussian has $F=3$. Increasing $F$ towards small scales indicates increasingly strong relative tails, although measurement noise and nonstationary mixtures also need checking.

A toy distribution isolates the rare-event effect. Let $X$ vanish with probability $1-p$ and take values $+\sigma /\sqrt{p}$ and $-\sigma /\sqrt{p}$ with probability $p/2$ each. ThenAt $p=0.05$, the variance is still ${\sigma }^2$ but the flatness is $20$. This is an illustrative marginal distribution, not a construction of a complete turbulent field.

Spacecraft measurements provide a concrete application. Analysis of Helios 2 magnetic and velocity records compared increments at different lags and heliocentric distances, finding scale-dependent flatness in both fast and slow solar wind. Mapping time lag to spatial separation requires an advection assumption. Flatness characterizes the fluctuations; by itself it does not establish the sign or magnitude of an energy cascade.^[ref]