Optimally time-dependent mode analysis of vortex gust-airfoil wake interactions

Identification of the transient dynamics is important for understanding the underlying physics of unsteady fluid flows. Such analysis is challenging for flows with unsteady base states. In this study, optimally time-dependent (OTD) modes, a set of orthonormal modes that traces the most amplified directions of the dynamics, are considered to study the primary transient flow features. We apply the OTD mode analysis to gust vortex-airfoil wake interactions, which exhibit strong transient amplification as the gust vortex convects over the airfoil. The OTD modes capture the transient instabilities related to the dynamic characteristics of the unsteady flow. Moreover, OTD modes with time-varying linear operators uncover transient modes induced by vortical interactions. This study provides physical insights into the time-evolving amplification modes for nonlinear, non-stationary flows with implications for active flow control of highly unsteady flows.