SUBHARMONIC TRANSITION TO TURBULENCE IN A FLAT-PLATE BOUNDARY-LAYER AT MACH-NUMBER-4.5

The subharmonic transition process of a flat-plate boundary layer at a free-stream Mach number of M(infinity) = 4.5 and a Reynolds number of 10000 based on freestream velocity and initial displacement thickness is investigated by direct numerical simulation up to the beginning of turbulence. A second-mode instability superimposed with random noise of low amplitude is forced initially. The secondary subharmonic instab ility evolves from the noise in accordance with theory and leads to a staggered Lambda-vortex pattern. Finite-amplitude Lambda-vortices init iate the build-up of detached high-shear layers below and above the cr itical layer. The detached shear-layer generation and break-up are con fined to the relative-subsonic part of the boundary layer. The breakdo wn to turbulence can be separated into two phases, the first being the breakup of the lower shear layer and the second being the break-up of the upper shear layer. Four levels of subsequent roll-up of the lower , Y-shaped shear layer have been observed, leading to new vortical str uctures which are unknown from transition at low Mach numbers. The upp er shear layer behaviour is similar to that of the well-known high-she ar layer in incompressible boundary-layer transition. It is concluded that, as in incompressible flow, turbulence is generated via a cascade of vortices and detached shear layers with successively smaller scale s. The different phases of shear-layer break-up are also reflected in the evolution of averaged quantities. A strong decrease of the shape f actor, as well as an increase of the skin friction coefficient, and a gradual loss of spanwise symmetry indicate the final breakdown to turb ulence, where the mean velocity and temperature profiles approach thos e measured in fully turbulent flow.