  Scale interaction is studied in wall-bounded turbulence by focusing on the
frequency modulation (FM) mechanism of large scales on small scale velocity
fluctuations. Differently from amplitude modulation analysis, frequency
modulation has been less investigated also due to the difficulty to develop
robust tools for broadband signals. To face this issue, the natural visibility
graph approach is proposed in this work to map the full velocity signals into
complex networks. We show that the network degree centrality is able to capture
the signal structure at local scales directly from the full signal, thereby
quantifying FM. Velocity signals from numerically-simulated turbulent channel
flows and an experimental turbulent boundary layer are investigated at
different Reynolds numbers. A correction of Taylor's hypothesis for time-series
is proposed to overcome the overprediction of near-wall frequency modulation
obtained when local mean velocity is used as the convective velocity. Results
provide network-based evidences of the large-to-small FM features for all the
three velocity components in the near-wall region, with a reversal mechanism
emerging far from the wall. Additionally, scaling arguments in the view of the
quasi-steady quasi-homogeneous hypothesis are discussed, and a delay-time
between large and small scales very close to the near-wall cycle characteristic
time is detected. Results show that the visibility graph is a parameter-free
tool that turns out to be effective and robust to detect FM in different
configurations of wall-bounded turbulent flows. Based on present findings, the
visibility network-based approach can represent a reliable tool to
systematically investigate scale interaction mechanisms in wall-bounded
turbulence.
