Spectra and pseudospectra of mean-linearized turbulent flow over dynamic surfaces

Carefully designed non-rigid surfaces have the potential to reduce the intensity and drag forces associated with turbulent flow across them. Here, we analyze the mean-linearized stability and energy amplification properties of such systems. This approach is motivated several prior works over the last decade applying resolvent analysis methods to study turbulent flow over surfaces featuring compliance and dynamic wall transpiration. This talk will first show that enabling surface compliance can introduce unstable eigenmodes to the mean-linearized dynamics, even in cases where energy amplification (i.e. resolvent gain) is seemingly suppressed. Next it will be demonstrated that even in cases where such systems are linearly stable, there can be eigenmodes introduced near the marginal stability threshold. We reveal that such eigenmodes can be associated with a counterintuitive nonmodal phenomena where there is a local maximum in the pseudospetra (corresponding to a minimum in the resolvent gain) in the vicinity of this marginally stable eigenvalue. We relate these findings to classical stability analysis results and to a classic counterexample concerning matrix pseudospectra, and further discuss the possible practical implications of these findings.