The variation of transition location in response to the variation of the amplitudes of initial disturbances

Abstract

The transition location of a boundary layer depends on the amplitude and characteristic of initial disturbances. The larger the amplitude and the amplification rate of the initial disturbances are, the more upstream the transition location is. However, the environment surrounding the flying vehicle is variable, so the amplitude and characteristic of the disturbances triggered in the boundary layer through receptivity are also variable. In this paper, how the transition location varies in response to the variation of the initial disturbance amplitudes is studied by using direct numerical simulation. The results show that if the initial disturbance amplitudes become smaller, the transition location moves downstream correspondingly, but there is a time delay compared to the time of arrival of the disturbances with reduced amplitudes. Moreover, the speed of moving downstream is appreciably lower than the propagation speed of the disturbances. On the other hand, if the amplitudes of the initial disturbances recover their original value, the transition would immediately take place whenever the disturbances reach the former transition location, but the laminar flow between the new and old transition locations would not become turbulent immediately. Theoretical explanations are provided based on the transition mechanism found by our group.