  In hydrodynamic (HD) turbulence an exact decomposition of the energy flux
across scales has been derived that identifies the contributions associated
with vortex stretching and strain self-amplification (P. Johnson, Phys. Rev.
Lett., 124, 104501 (2020), J. Fluid Mech. 922, A3 (2021)) to the energy flux
across scales. Here we extend this methodology to general coupled
advection-diffusion equations, in particular to homogeneous magnetohydrodynamic
(MHD) turbulence, and we show that several subfluxes are related to each other
by kinematic constraints akin to the Betchov relation in HD. Applied to data
from direct numerical simulations, this decomposition allows for an
identification of physical processes and for the quantification of their
respective contributions to the energy cascade, as well as a quantitative
assessment of their multi-scale nature through a further decomposition into
single- and multi-scale terms. We find that vortex stretching is strongly
depleted in MHD compared to HD, and the kinetic energy is transferred from
large to small scales almost exclusively by the generation of regions of
small-scale intense strain induced by the Lorentz force. In regions of large
strain, current sheets are stretched by large-scale straining motion into
regions of magnetic shear. This magnetic shear in turn drives extensional flows
at smaller scales. Magnetic energy is transferred from large to small scales,
albeit with considerable backscatter, predominantly by the aforementioned
current-sheet thinning in region of high strain while the contribution from
current-filament stretching - the analogue to vortex stretching - is
negligible. Consequences of these results to subgrid-scale turbulence modelling
are discussed.
