  Turbulent flows in the presence of walls may be apprehended as a collection
of momentum- and energy-containing eddies (energy-eddies), whose sizes differ
by many orders of magnitude. These eddies follow a self-sustaining cycle, i.e.,
existing eddies are seeds for the inception of new ones, and so forth.
Understanding this process is critical for the modelling and control of
geophysical and industrial flows, in which a non-negligible fraction of the
energy is dissipated by turbulence in the immediate vicinity of walls. In this
study, we examine the causal interactions of energy-eddies in wall-bounded
turbulence by quantifying how the knowledge of the past states of eddies
reduces the uncertainty of their future states. The analysis is performed via
direct numerical simulation (DNS) of turbulent channel flows in which
time-resolved energy-eddies are isolated at a prescribed scale. Our approach
unveils, in a simple manner, that causality of energy-eddies in the buffer and
logarithmic layers is similar and independent of the eddy size. We further show
an example of how novel flow control and modelling strategies can take
advantage of such self-similar causality.
