The Lagrangian frequency spectrum as a diagnostic for magnetohydrodynamic turbulence dynamics

For the phenomenological description of magnetohydrodynamic turbulence competing models exist, e.g. Boldyrev [Phys.Rev.Lett. 96, 115002, 2006] and Gogoberidze [Phys.Plas. 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 timescale of the turbulent fluctuations, τac, and the associated cascade timescale, τcas. Thus, the Lagrangian energy spectrum can serve to identify weak (τac τcas) and strong (τac ∼ τcas) interaction mechanisms providing insight into the turbulent energy cascade. The new approach is illustrated by results from direct numerical simulations of twoand three-dimensional incompressible MHD turbulence.