k 8 3 Spectrum in Kinetic Alfvén Wave Turbulence: Implications for the Solar Wind

The nature of solar wind turbulence at large scale is rather well understood in the theoretical framework of magnetohydrodynamics. The situation is quite different at subproton scales where the magnetic energy spectrum measured by different spacecraft does not fit with the classical turbulence predictions: a power-law index close to −8/3 is generally reported, which is far from the predictions of strong and wave turbulence, −7/3 and −5/2, respectively. This discrepancy is considered as a major problem for solar wind turbulence. Here, we show with a nonlinear diffusion model of weak kinetic Alfvén wave turbulence where the cascade is driven by local triadic interactions that a magnetic spectrum with a power-law index of −8/3 can emerge. This scaling corresponds to a self-similar solution of the second kind with a front propagation following the law kf ∼ (t*−t)−3/4, with t < t*. This solution appears when we relax the implicit assumption of stationarity generally made in turbulence. The agreement between the theory and observations can be interpreted as an evidence of the nonstationarity of solar wind turbulence at subproton scales.