Input-output analysis of transitional channel flow over large-scale wavy walls

Flow over complex terrains is important in environmental applications such as understanding pollution transport in mountainous regions and flow over tree canopies. Surface roughness also plays an important role in industrial applications such as riblets that alter eddies in turbulent flows and potentially reduce the drag. This work analyzes flow over large-scale wavy walls as a low-order approximation to understand the roughness effect with a dominant wavelength. We conduct input-output analysis of transitional channel flow over large-scale wavy walls, where the wavy wall is included through implementing volume penalization method for the solid domain. The Chebyshev collocation method is used in wall-normal direction and the Fourier collocation method is employed in the wavy direction of the topography. Input-output analysis allows us to identify the dominant wavenumber frequency pair leading to the largest response. We also employ singular value decomposition to obtain the leading forcing and response mode, which shows a smaller wavelength than the length scale of the wavy wall.