Intermittency in Weak Magnetohydrodynamic Turbulence

Intermittency is investigated using decaying direct numerical simulations of incompressible weak magnetohydrodynamic turbulence with a strong uniform magnetic field ${\bf b_0}$ and zero cross-helicity. At leading order, this regime is achieved via three-wave resonant interactions with the scattering of two of these waves on the third/slow mode for which $k_{\parallel} = 0$. When the interactions with the slow mode are artificially reduced the system exhibits an energy spectrum with $k_{\perp}^{-3/2}$, whereas the expected exact solution with $k_{\perp}^{-2}$ is recovered with the full nonlinear system. In the latter case, strong intermittency is found when the vector separation of structure functions is taken transverse to ${\bf b_0}$ - at odds with classical weak turbulence where self-similarity is expected. This surprising result, which is being reported here for the first time, may be explained by the influence of slow modes whose regime belongs to strong turbulence. We derive a new log--Poisson law, $\zeta_p = p/8 +1 -(1/4)^{p/2}$, which fits perfectly the data and highlights the dominant role of current sheets.