  In incompressible and periodic statistically stationary turbulence, exchanges
of turbulent energy across scales and space are characterised by very intense
and intermittent spatio-temporal fluctuations around zero of the
time-derivative term, the spatial turbulent transport of fluctuating energy,
and the pressure-velocity term. These fluctuations are correlated with each
other and with the intense intermittent fluctuations of the interscale energy
transfer rate. These correlations are caused by the sweeping effect, the link
between non-linearity and non-locality, and also relate to geometrical
alignments between the two-point fluctuating pressure force difference and the
two-point fluctuating velocity difference in the case of the correlation
between the interscale transfer rate and the pressure-velocity term. All these
processes are absent from the spatio-temporal average picture of the turbulence
cascade in statistically stationary and homogeneous turbulence.
