Two-dimensional boundary layer flows in quiet disturbance environments are known to become unstable to Tollmien–Schlichting waves. The experimental work of Liepmann et al. (J Fluid Mech 118:187–200, 1982), Liepmann and Nosenchuck (J Fluid Mech 118:201–204, 1982) showed how it is possible to control and reduce unstable Tollmien–Schlichting wave amplitudes using unsteady surface heating. We consider the problem of an oncoming planar compressible subsonic boundary layer flow with a three-dimensional vibrator mounted on a flat plate, and with surface heating present. It is shown using asymptotic methods based on triple-deck theory that it is possible to choose an unsteady surface heating distribution to cancel out the response due to the vibrator. An approximation based on the exact formula is used successfully in numerical computations to confirm the findings. The results presented here are a generalisation of the analogous results for the two-dimensional problem in Brennan et al. (J Fluid Mech 909:A16-1, 2020).

众所周知，在安静的扰动环境中二维边界层流对于Tollmien-Schlichting波变得不稳定。Liepmann等人的实验工作。Liepmann和Nosenchuck（J Fluid Mech 118：187–200，1982），Liepmann和Nosenchuck（J Fluid Mech 118：201–204，1982）展示了如何使用不稳定的表面加热来控制和减小不稳定的Tollmien-Schlichting波幅。我们考虑到将三维振动器安装在平板上并存在表面加热的情况下，即将到来的平面可压缩亚音速边界层流动的问题。使用基于三层理论的渐近方法表明，可以选择一个不稳定的表面加热分布来抵消由于振动器引起的响应。基于精确公式的近似值已成功用于数值计算中，以确认发现。这里介绍的结果是Brennan等人针对二维问题的类似结果的概括。（J Fluid Mech 909：A16-1，2020）。