Em. Saiki et al., SPATIAL SIMULATION OF SECONDARY INSTABILITY IN PLANE CHANNEL FLOW - COMPARISON OF K-TYPE AND H-TYPE DISTURBANCES, Journal of Fluid Mechanics, 253, 1993, pp. 485-507
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.