  Using two- and three-dimensional hydromagnetic simulations for a range of
different flows, including laminar and turbulent ones, it is shown that
solutions expressing the field in terms of Euler potentials (EP) are in general
incorrect if the EP are evolved with an artificial diffusion term. In three
dimensions, standard methods using the magnetic vector potential are found to
permit dynamo action when the EP give decaying solutions. With an imposed
field, the EP method yields excessive power at small scales. This effect is
more exaggerated in the dynamic case, suggesting an unrealistically reduced
feedback from the Lorentz force. The EP approach agrees with standard methods
only at early times when magnetic diffusivity did not have time to act. It is
demonstrated that the usage of EP with even a small artificial magnetic
diffusivity does not converge to a proper solution of hydromagnetic turbulence.
The source of this disagreement is not connected with magnetic helicity or the
three-dimensionality of the magnetic field, but is simply due to the fact that
the nonlinear representation of the magnetic field in terms of EP that depend
on the same coordinates is incompatible with the linear diffusion operator in
the induction equation.
