On the Issue of the Nonlinear Theory of the Instability Waves

Summary

The method of matching asymptotic expansions is used to investigate the nonlinear nonstationary waves with nonlinear critical layer. The structure of the nonlinear nonstationary critical layer is studied. The time function of the wave amplitude has been obtained.

The subject of the theory of the nonlinear development of the disturbances in the boundary layer remains to be the key subject for understanding the mechanism of the boundary layer transition to turbulence. It was Lin C.C. who noted, that if a nondimensional amplitude of the disturbance ε is greater than ε*=(αRe)^−2/3, Then the nonlinear effects in the critical layer (C.L.), that is, where the phase velocity of the disturbance equals the basic flow velocity, become basic. Waves with nonlinear C.L. were first considered in [1]–[3].