Nonlinear stability of the compressible attachment-line boundary layer

Abstract

Transition to turbulence of flow around a wing can be triggered by the instability at the leading edge. Such a flow can be modeled using a base flow with perturbations superimposed on it. The nonlinear evolution of three dimensional perturbations of the compressible attachment-line boundary layer is studied, which forms an extension of two-dimensional nonlinear calculations of previous researchers based upon the Görtler-Hämmerlin assumption. A comparison has been made between the evolution of symmetric disturbances and the case where no restriction on the shape of the perturbations was imposed.

It has been found that, for general disturbances, the results start to deviate significantly from linear stability theory for disturbance levels of about 1%. At these disturbance levels the growth rate starts to increase to a much higher value. The behaviour of the u- and the T-disturbances seems to be entirely responsible for the deviation from linear theory. However, when only symmetric modes are allowed in the simulations, the sudden increase of the growth rate is absent. Therefore, the interaction between symmetric and antisymmetric modes is likely to be responsible for the sudden increase of the growth rate.