  We investigate numerically the dynamics of two-dimensional Euler and ideal
magnetohydrodynamics (MHD) flows in systems with a finite number of modes, up
to $4096^2$, for which several quadratic invariants are preserved by the
truncation and the statistical equilibria are known. Initial conditions are the
Orszag-Tang vortex with a neutral X-point centered on a stagnation point of the
velocity field in the large scales. In MHD, we observe that the total energy
spectra at intermediate times and intermediate scales correspond to the
interactions of eddies and waves, $E_T(k)\sim k^{-3/2}$. Moreover, no
dissipative range is visible neither for Euler nor for MHD in two dimensions;
in the former case, this may be linked to the existence of a vanishing
turbulent viscosity whereas in MHD, the numerical resolution employed may be
insufficient. When imposing a uniform magnetic field to the flow, we observe a
lack of saturation of the formation of small scales together with a significant
slowing-down of their equilibration, with however a cut-off independent partial
thermalization being reached at intermediate scales.
