Floquet Analysis of Secondary Instability in Shear Flows

In previous work, the parametric excitation of secondary, three-dimensional disturbances in the Blasius boundary layer was investigated using the concept of temporal growth. The analysis was restricted to fundamental (peak-valley splitting) modes and subharmonic modes, i.e. to disturbances with the same or twice the streamwise wavelength of the primary TS wave. Here, we generalize these studies in two directions. First, we analyze the spatial growth of secondary disturbances and develop an analogue of Gaster’s transformation. Second, we study the secondary instability with respect to detuned modes, i.e. disturbances with arbitrary streamwise wavelength, and relate the results to observations of subharmonic and combination resonance in the flat-plate boundary layer. As a by-product, we show the rapid convergence of the Fourier series that governs the streamwise structure of the disturbances.