Mean and unsteady flow reconstruction using data-assimilation and resolvent analysis

A methodology is presented that exploits both data-assimilation techniques and resolvent analysis for reconstructing turbulent flows, containing organized structures, with an efficient set of measurements. The mean (time-averaged) flow is obtained using variational data-assimilation that minimizes the discrepancy between a limited set of flow measurements, generally from an experiment, and a numerical simulation of the Navier–Stokes equations. The fluctuations are educed from resolvent analysis and time-resolved data at a single point in the flow. Resolvent analysis also guides where measurements of the mean and fluctuating quantities are needed for efficient reconstruction of a simple example case study: flow around a circular cylinder at a Reynolds number of Re 100. For this flow, resolvent analysis reveals that the leading singular value, most amplified modes, and the mean profile for 47 < Re < 320 scale with the shedding frequency and length of the recirculation bubble. A relationship between these two parameters reinforces the notion that a wave maker, for which the length scales with the recirculation bubble, determines the frequency and region where an instability mechanism is active. The procedure offers a way to choose sensor locations that capture the main coherent structures of a flow and a method for computing mean pressure by using correctly weighted resolvent modes.