Kolmogorov Vectorial Law for Solar Wind Turbulence

We investigate a class of axisymmetric magnetohydrodynamic turbulence which satisfies the exact relation for third-order Elsässer structure functions. Following the critical balance conjecture, we assume the existence of a power-law relation between correlation length scales along and transverse to the local mean magnetic field direction. The flow direction of the vector third-order moments F ± is then along axisymmetric concave/convex surfaces, the axis of symmetry being given by the mean magnetic field. Under this consideration, the vector F ± satisfies a simple Kolmogorov law which depends on the anisotropic parameter a ± , which measures the concavity of the surfaces. A comparison with recent in situ multispacecraft solar wind observations is made; it is concluded that the underlying turbulence is very likely convex. A discussion is given about the physical meaning of such an anisotropy.