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 nonlinearity 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.
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