For the phenomenological description of magnetohydrodynamic turbulence competing models exist, e.g., Boldyrev [Phys. Rev. Lett. 96, 115002 (2006)] and Gogoberidze [Phys. Plasmas 14, 022304 (2007)], which predict the same Eulerian inertial-range scaling of the turbulent energy spectrum although they employ fundamentally different basic interaction mechanisms. A relation is found that links the Lagrangian frequency spectrum with the autocorrelation time scale of the turbulent fluctuations ${\tau }_{\mathrm{ac}}$ and the associated cascade time scale ${\tau }_{\mathrm{cas}}$. Thus, the Lagrangian energy spectrum can serve to identify weak (${\tau }_{\mathrm{ac}}\ll {\tau }_{\mathrm{cas}}$) and strong (${\tau }_{\mathrm{ac}}\sim {\tau }_{\mathrm{cas}}$) interaction mechanisms providing insight into the turbulent energy cascade. The new approach is illustrated by results from direct numerical simulations of two- and three-dimensional incompressible MHD turbulence.

• Received 6 September 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.235005