Secondary instability of laminar flows

The kinematic wave theory, which was developed originally for nondissipative wave systems, is modified for the analysis of a dissipative wave system in a slightly inhomogeneous medium. The modification is made for application to the problem of predicting the development of a high-frequency wavepacket in an unsteady laminar flow, which consists of a steady flow and a low-frequency primary wave travelling in a streamwise direction. It is shown that secondary instability of the laminar flow takes the form of continuous evolution of the wavepacket when the group velocity of secondary disturbances with a specific frequency coincides with the phase velocity of the primary wave. This condition is attained at a certain value of the primary-wave amplitude. A numerical calculation is made for rough estimation of the critical amplitude and phase velocity on the assumption that the primary wave is of the Tollmien-Schlichting type.