Non-linear scale interactions in a forced turbulent boundary layer*

A strong phase-organizing influence exerted by a single synthetic large-scale spatio-temporal mode on directly-coupled (through triadic interactions) small scales in a turbulent boundary layer forced by a spatially-impulsive dynamic wall-roughness patch was previously demonstrated by the authors (\emph{J. Fluid Mech.} 2015, \emph{vol.} 767, R4). The experimental set-up was later enhanced to allow for simultaneous forcing of multiple scales in the flow. Results and analysis are presented from a new set of novel experiments where two distinct large scales are forced in the flow by a dynamic wall-roughness patch. The internal non-linear forcing of two other scales with triadic consistency to the artificially forced large scales, corresponding to sum and difference in wavenumbers, is dominated by the latter. This allows for a forcing-response (input-output) type analysis of the two triadic scales, and naturally lends itself to a resolvent operator based model (e.g. McKeon \& Sharma, \emph{J. Fluid Mech.} 2010, \emph{vol.} 658, \emph{pp.} 336-382) of the governing Navier-Stokes equations.