Resolvent and Spectral POD Analyses of a Laminar Separation Bubble

Resolvent analysis is an increasingly popular technique capable of providing insight about the input-output characteristics of a given fluid flow at a specified frequency and wavenumber. Moreover, the resolvent of the linearized Navier-Stokes operator can be used to compute the pseudospectrum, which can be important for non-normal operators as often arise in shear flows.

Direct numerical simulations are performed for three-dimensional laminar boundary layer flow in which suction and blowing are imposed at the top of the computational domain to generate a separation bubble at the bottom surface. The linear input-output (resolvent) operator is computed relative to the spanwise- and time-averaged mean flow, and the optimal forcing and response modes are obtained via a randomized singular value decomposition. The resulting forcing modes illustrate regions where the flow is most sensitive to perturbations. The corresponding response modes are compared with spectral (frequency-domain) POD modes obtained from snapshots of the direct numerical simulations, and the two sets of modes show similar features.