SPATIAL SIMULATION OF SECONDARY INSTABILITY IN PLANE CHANNEL FLOW - COMPARISON OF K-TYPE AND H-TYPE DISTURBANCES

This study involves a numerical simulation of spatially evolving secon dary instability in plane channel flow. The computational algorithm in tegrates the time-dependent, three-dimensional, incompressible Navier- Stokes equations by a mixed finite-difference/spectral technique. In p articular, we are interested in the differences between instabilities instigated by Klebanoff (K-) type and Herbert (H-) type inflow conditi ons, and in comparing the present spatial results with previous tempor al models. It is found that for the present inflow conditions, H-type instability is biased towards one of the channel walls, while K-type i nstability evolves on both walls. For low initial perturbation amplitu des, H-type instability exhibits higher growth rates than K-type insta bility while higher initial amplitudes lead to comparable growth rates of both H- and K-type instability. In H-type instability, spectral an alysis reveals the presence of the subharmonic two-dimensional mode wh ich promotes the growth of the three-dimensional spanwise and fundamen tal modes through nonlinear interactions. An intermodal energy transfe r study demonstrates that there is a net energy transfer from the thre e-dimensional modes to the two-dimensional mode. This analysis also in dicates that the mean mode transfers net energy to the two-dimensional subharmonic mode and to the three-dimensional modes.