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Bruno Bavassano is a solar wind researcher whose publications connect spacecraft observations with the statistical behavior of magnetohydrodynamic turbulence. A 2003 study with Roberto Bruno, Vincenzo Carbone and Luca Sorriso-Valvo compared velocity and magnetic field fluctuations between $0.3$ and $1$ astronomical unit from the Sun. It separated fast from slow solar wind, and changes in field magnitude from changes in field direction.^[ref]

The diagnostic was scale-dependent kurtosis. For a fluctuation $X$ with mean zero, $K=\mathbb{E}[X^4]/\mathbb{E}[X^2{]}^2$ weights rare large events strongly. A Gaussian distribution has $K=3$; a rising value as the separation shrinks indicates that small-scale changes are becoming more unevenly distributed. The study found stronger intermittency in compressive magnetic fluctuations than in the corresponding velocity fluctuations, and a radial increase in fast-wind intermittency.^[ref]

For intuition, replacing one ordinary increment by an increment ten times larger multiplies its contribution to the fourth moment by $10^4$, rather than $10^2$ for its squared contribution. This is why a sparse set of sharp changes can matter even when most samples look modest.

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]