Flow Separation and Control

Periodic low-order roughness has been widely used to analyze flow behavior over complex terrains, such as dunes in deserts, hills, and valleys, which is important for wind energy and environmental applications. In this work, we utilize the volume penalty method as a fluid-structure interaction tool to understand separated flow over streamwise wavy walls. The volume penalty method has been incorporated into direct numerical simulation (DNS) to model the streamwise wavy walls. The volume penalty term is modeled by an error function, leading to a smooth transition across the fluid-solid interface with a certain thickness. Our DNS can reproduce the recirculation due to the separation induced by the streamwise wavy wall. The laminar base flow obtained from DNS is used in the input-output analysis, where we employ the same volume penalty method as our DNS to model streamwise wavy walls. Our analysis identifies the most sensitive forcing and response modes of separated flow over streamwise wavy walls and examines the influence of spatiotemporal scales of flow structures on forcing and response modes. As the frequency increases, the response mode and the forcing mode have a smaller length scale in the streamwise direction. At higher spanwise wavenumbers, the flow structures break down into smaller structures, while at lower spanwise wavenumbers, larger dominant structures are preserved.