  This study shows the connection between three previously observed but
seemingly unrelated phenomena in hydrodynamic (HD) and magnetohydrodynamic
(MHD) turbulent flows, involving the emergence of fluctuations occurring on
very long time scales: the low-frequency 1/f noise in the power frequency
spectrum, the delayed ergodicity of complex valued amplitude fluctuations in
wavenumber space, and the spontaneous flippings or reversals of large scale
fields. Direct numerical simulations of ideal MHD and HD are employed in three
space dimensions, at low resolution, for long periods of time, and with high
accuracy to study several cases: Different geometries, presence of rotation
and/or a uniform magnetic field, and different values of the associated
conserved global quantities. It is conjectured that the origin of all these
long-time phenomena is rooted in the interaction of the longest wavelength
fluctuations available to the system with fluctuations at much smaller scales.
The strength of this non-local interaction is controlled either by the
existence of conserved global quantities with a back-transfer in Fourier space,
or by the presence of a slow manifold in the dynamics.
