  This paper develops a spatial input-output approach to investigate the
dynamics of a turbulent boundary layer subject to a localized single frequency
excitation. This method uses one-way spatial integration to reformulate the
problem in terms of spatial evolution equations. The technique is used to
examine the effect of localized periodic actuation at a given temporal
frequency, based on an experimental set-up in which an active large-scale is
introduced into the outer layer of a turbulent boundary layer. First, the
large-scale structures associated with the phase-locked modal velocity field
obtained from spatial input-output analysis are shown to closely match those
computed based on hot-wire measurements. The approach is then used to further
investigate the response of the boundary layer to the synthetically generated
large-scale. A quadrant trajectory analysis indicates that the spatial
input-output response produces shear stress distributions consistent with those
in canonical wall-bounded turbulent flows in terms of both the order and types
of events observed. The expected correspondence between the dominance of
different quadrant behavior and actuation frequency is also observed. These
results highlight the promise of a spatial input-output framework for analyzing
the formation and streamwise evolution of structures in actuated wall-bounded
turbulent flows.
