Characteristics of nonlinear evolution of wavepackets in boundary layers

Abstract

The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al. using direct numerical simulation (DNS). It was found that certain small-scale 3-D disturbances amplified rapidly. These disturbances exhibit the characteristics of second modes, and the most amplified components have a well-defined spanwise wavelength, indicating a clear selectivity of the amplification. In the case of a cone, the three-dimensionality of the base flow and the disturbances themselves may be responsible for the rapid amplification. In order to ascertain which of these two effects are essential, in this study we carried out DNS of the nonlinear evolution of a spanwise localized disturbance (wavepacket) in a flat-plate boundary layer. A similar amplification of small-scale disturbances was observed, suggesting that the direct reason for the rapid amplification is the three-dimensionality of the disturbances rather than the three-dimensional nature of the base flow, even though the latter does alter the spanwise distribution of the disturbance. The rapid growth of 3-D waves may be attributed to the secondary instability mechanism. Further simulations were performed for a wavepacket of first modes in a supersonic boundary layer and of Tollmien-Schlichting (T-S) waves in an incompressible boundary layer. The results show that the amplifying components are in the band centered at zero spanwise wavenumber rather than at a finite spanwise wavenumber. It is therefore concluded that the rapid growth of 3-D disturbances in a band centered at a preferred large spanwise wavenumber is the main characteristic of nonlinear evolution of second mode disturbances in supersonic boundary layers.