Excitation and development of instability in a compressible boundary layer as obtained in high-order accurate numerical simulation without introducing artificial perturbations

The nonstationary Navier–Stokes equations describing the instability of the boundary layer on a plate placed instantaneously in a subsonic flow are solved numerically using a scheme with 16th-order multioperator approximations. The problem is considered in the traditional formulation without introducing instability exciters. Unstable modes arise due to the controlled background of small perturbations of the exact solutions produced by the truncation errors of the scheme. The presented solutions describe a scenario in which packets of Tollmien–Schlichting waves of time-dependent intensity develop near the leading edge of the plate and propagate downstream with increasing amplitudes. The influence exerted by the spectral content of the dissipative part of the scheme on the wave numbers and the amplitudes of the wave packets is estimated. The correspondence between the instability development in the resulting solutions and the basic results of linear theory is discussed.