On the connection between resolvent analysis and forced optimally time-dependent decomposition

This presentation addresses a new methodology for identifying the most responsive forcing and the most receptive states of a dynamical system. To this end, sensitivity analysis with forced optimally time-dependent (f-OTD) modes is introduced. With only the knowledge of the steady base flow or the mean flow, we establish a connection between f-OTD and resolvent analysis. The key observation is that the dominant f-OTD modes converge to the most responsive and forcing modes of the resolvent operator. We further demonstrate the ability of the f-OTD to compute the system response to an arbitrary forcing with an arbitrary time-dependent base flow. The theoretical results are demonstrated in two cases: the Burgers' equation and the temporally evolving jet.