| As is well known, the problem of laminar-turbulent transition in a boundary layer is very important from practical application point of view. In most cases, transition starts from the growth of small amplitude disturbance waves. When the disturbance amplitude reaches a certain magnitude, nonlinear effect starts to play a role. For incompressible boundary layer or plane channel flow, typical three-dimensional structures would appear. By flow visualization, it was found that the structures looked like the Greek letterΛ. There are two different kinds of -structure, namely, Klebanoff type structure (K-type structure), for which the stream-wise period is the same as those of T-S wave, And sub-harmonic or N-type structure, for which the stream-wise period is twice as much as those of T-S wave, hence corresponds to a certain sub-harmonic wave. N-type can be further divided as C(Craik)-type and H(Herbert)-type.Sub-harmonic waves have been detected in certain transition experiments for supersonic flow. However, data are not plenty and lake of details.In this paper, lamina-turbulent transition of a supersonic boundary layer was examined by numerically solving the N-S equation, to see if the same mechanism existed for the generation of sub-harmonic waves. The results showed that when a pair of oblique waves were introduced at the entrance, their non-linear interaction would trigger the rapid growth of stream-wise vortex and other harmonics, while themselves kept only linear growth. When a pair of oblique waves and a 2-D T-S wave, satisfying resonant condition, were introduced at the entrance, the oblique waves and other harmonics would grow rapidly. When a 2-D T-S wave and a three-dimensional wave with its frequency half of the 2-D T-S wave, it was found that secondary instability did exist. The relation between the growth rate of the 3-D wave and the amplitude of the 2-D wave, as well as the span-wise wave number, has also been studied.
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