  We report on a numerical observation of recurrence phenomenon in a three
dimensional magneto-hydrodynamic (MHD) plasma for certain classes of initial
flow profiles. Our simulations discover such a behaviour for an initial
Taylor-Green (TG) type of flow whereas under identical conditions an initial
Arnold-Beltrami-Childress (ABC) flow fails to show recurrent behaviour. This
difference in the dynamical behaviours is traced to the nature of the Rayleigh
quotient in each case. The Rayleigh quotient which is an approximate measure of
the number of active degrees of freedom in a dynamical system is found to
remain small and bounded in time for the TG flow but grows indefinitely in time
for the ABC flow. An estimate of the effective degrees of freedom for the TG
flow case is provided and its practical implications for the nonlinear
behaviour of the continuum nonlinear MHD plasma system is discussed.
