Observation of Inertial Energy Cascade in Interplanetary Space Plasma

Direct evidence for the presence of an inertial energy cascade, the most characteristic signature of hydromagnetic turbulence (MHD), is observed in the solar wind by the Ulysses spacecraft. After a brief rederivation of the equivalent of Yaglom’s law for MHD turbulence, a linear relation is indeed observed for the scaling of mixed third-order structure functions involving Elsässer variables. This experimental result firmly establishes the turbulent character of low-frequency velocity and magnetic field fluctuations in the solar wind plasma.

Figure 1

The scaling behavior of $Y^{\pm }(\tau )$ as a function of the time scale $\tau$ for four different periods we examined. Different colors of the curves refer to positive and negative values of the mixed structure functions $Y^{\pm }(\tau )$ and thus of ${ϵ}^{\pm }$. The full black lines correspond to linear scaling laws to guide the eye.

Figure 2

Hourly averaged quantities are represented as a function of the flight time of Ulysses. The top panels represent, respectively, the solar wind speed, the magnitude of the magnetic field, the particle density, the distance from the Sun and the heliolatitude angle. In the bottom panel are plotted the values of ${ϵ}^{\pm }$, calculated through a fit using the relation (3) during the periods where a clear linear scaling exists.