Dual velocity-component investigation of transient growth in the Blasius boundary layer

Abstract

Transient growth of finite three-dimensional perturbations in wall-bounded laminar shear flows has been extensively studied theoretical, numerical and experimentally. With regard to the experimental work, the vast majority of the investigations have been focused only on the behaviour of the streamwise velocity component, u', despite the importance of the spanwise gradient of the wall-normal velocity component, [Symbols appear here. To view, please open pdf attachment], as the forcing agent. The present study provides a step forward in the experimental characterisation of transient growth providing, by Laser Doppler Anemometry, simultaneous and highly spatially resolved measurements of both streamwise and wall-normal velocity components of three-dimensional disturbances embedded in a two-dimensional laminar boundary layer. The disturbances are deterministic, as they are generated by a spanwise array of cylindrical roughness elements. The readings are concentrated in both the wake and u'-energy growth regions. Contrary to non-normal operator theory, which describes transient growth as a linear mechanism, a spectral analysis in the present study demonstrates that there exists an underlying non-linear mechanism. This non-linear behaviour is attributed to the influence of the wake in the u'-energy growth region. Numerical simulations considering non-linear terms confirm this conclusion. Both spectral and wavelet analyses have been conducted, providing information regarding the spatial location of the components of the perturbation as well as the relationship between the scales of motion. The numerical simulations are also employed as a workbench to design actuators for open-loop control of transient growth.