Modal analysis of coherent structures in a self-similar turbulent boundary layer with adverse pressure gradient

Local linear stability analysis as well as Fourier transform and proper orthogonal decomposition are applied to a self-similar turbulent boundary layer on a flat plate with strong adverse pressure gradient to identify coherent structures. The modal analysis is based on data from direct numerical simulations. Coherent structures are identified at the wall-normal position that coincides with an inflection point in the streamwise mean velocity profile. It is found that these coherent structures are governed by broadband Kelvin–Helmholtz instabilities, which are linearly unstable for a certain self-similar frequency range, leading to spatial amplification in streamwise direction before they decay downstream. A very particular challenge is faced due to the limited time length of the dataset compared to the characteristic timescales of interest. Likewise, the spatial extent in streamwise direction limits the large observable wavelengths of interest. This issue is coped with by applying a Fourier transform in time combined with subsequent proper orthogonal decompositions in streamwise and spanwise direction to extract the statistically most correlated and coherent modes in the turbulent boundary layer.