-8/3 spectrum in kinetic Alfvén wave turbulence: implications for the solar wind

Abstract

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 sub-proton scales where the magnetic energy spectrum measured by different spacecrafts 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 (Passot and Sulem, 2019), 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 $k_f\sim (t_{\ast }-t{)}^{-3/4}$, with $t<t_{\ast }$. 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 non-stationarity of solar wind turbulence at sub-proton scales.

arXiv comment6 pages, 4 figures

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Cited by in corpus (6)

• Energy cascade rate measured in a collisionless space plasma with MMS data and compressible Hall magnetohydrodynamic turbulence theory
• The Ion Transition Range of Solar Wind Turbulence in the Inner Heliosphere: Parker Solar Probe Observations
• Direct Evidence of a Dual Cascade in Gravitational Wave Turbulence
• Wave Turbulence in Inertial Electron Magnetohydrodynamics
• Exact solution to the main turbulence problem for a compressible medium and the universal -8/3 turbulence spectrum of breaking waves
• Locality of triad interaction and Kolmogorov constant in inertial wave turbulence