In this paper we study the effect of subtle changes in initial conditions on
the evolution of global quantities in two-dimensional Magnetohydrodynamic (MHD)
turbulence. We find that a change in the initial phases of complex Fourier
modes of the Els\"{a}sser variables, while keeping the initial values of total
energy, cross helicity and Alfv\'{e}n ratio unchanged, has a significant effect
on the evolution of cross helicity. On the contrary, the total energy and
Alfv\'{e}n ratio are insensitive to the initial phases. Our simulations are
based on direct numerical simulation using the pseudo-spectral method.Comment: 12 pages LateX, 11 ps figures. Accepted for publication by Physics of
Plasma