Spatial Input–Output Analysis of Actuated Turbulent Boundary Layers

Abstract

This paper develops a spatial input–output approach to investigate the dynamics of a turbulent boundary layer subject to a localized single frequency excitation. One-way spatial integration is used to reformulate the problem in terms of spatial evolution equations. The associated input-output operator is then used to examine the effect of localized periodic actuation at a given temporal frequency, based on an experimental setup in which an active large scale structure 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 structures. 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.