  We investigate the underlying physics behind the change in amplitude
modulation coefficient in non-canonical wall-bounded flows in the framework of
the inner-outer interaction model (IOIM) (Baars et al., Phys. Rev. Fluids 1
(5), 054406). The IOIM captures the amplitude modulation effect, and here we
focus on extending the model to non-canonical flows. An analytical relationship
between the amplitude modulation coefficient and IOIM parameters is derived,
which is shown to capture the increasing trend of the amplitude modulation
coefficient with an increasing Reynolds number in a smooth-wall dataset. This
relationship is then applied to classify and interpret the non-canonical
turbulent boundary layer results reported in previous works. We further present
the case study of a turbulent boundary layer after a rough-to-smooth change.
Both single-probe and two-probe hotwire measurements are performed to acquire
streamwise velocity time series in the recovering flow on the downstream smooth
wall. An increased coherence between the large-scale motions and the
small-scale envelope in the near-wall region is attributed to the stronger
footprints of the over-energetic large-scale motions in the outer layer,
whereas the near-wall cycle and its amplitude sensitivity to the superposed
structures are similar to that of a canonical smooth-wall flow. These results
indicate that the rough-wall structures above the internal layer interact with
the near-wall cycle in a similar manner as the increasingly energetic
structures in a high-Reynolds number smooth-wall boundary layer.
