Numerical simulation of boundary-layer transition at Mach two

The linear and early nonlinear stages of boundary-layer transition at free-stream Mach number M_∞==2.0 are investigated by direct numerical simulation of the compressible Navier-Stokes equations. Results from simulations with a large computational box and small-amplitude random initial conditions are compared with linear stability theory. The growth rates of oblique waves are reproduced correctly. Two-dimensional waves show a growth that is modulated in time, indicating the presence of an extra unstable mode which moves supersonically relative to the free stream. Further simulations are conducted to investigate the nonlinear development of two- and three-dimensional disturbances The transition due to oblique disturbance waves is the most likely cause of transition at this Mach number, and is found to lead to the development of strong streamwise vortices.