Biglobal input–output analysis of separated flow over a periodic hill

This paper performs a biglobal input–output analysis of the separated flow over a periodic hill to understand the flow sensitivity to disturbances. We use the volume penalty method to model the solid body of the periodic hill, which is implemented in a spectral solver to obtain the two-dimensional base flow used in the biglobal input–output analysis. We formulate the spatiotemporal frequency response operator using the tensor product, and conduct singular value decomposition of this frequency response operator to identify the dominant response mode, forcing mode and input–output amplification. Results show that disturbances with high temporal frequencies result in shear-dominant flow structures with a smaller length scale, while as the temporal frequency approaches zero, the response modes are less oscillatory in the spatial domain and display global recirculation. With an increase in the spanwise wavenumber of disturbances, flow structures grow in length scale and become less oscillatory in space, while the amplification increases and then decreases with increasing spanwise wavenumber. In general, forcing modes show a peak near the separation region downstream of the hill crest, while the response modes show a peak near the reattachment region upstream of the hill crest.