Toward data-driven transient growth analysis

Non-modal stability analysis plays a crucial role in understanding bypass transition by identifying transient growth arising from the linearized Navier-Stokes operator. Typically, these analyses require access to temporal or spatial propagation operators that are not always easily obtained, especially for multi-physics problems. In this study, we propose an exclusively data-driven approach for transient growth analysis. Our method is derived by solving an optimization problem for the most amplified input and output modes that lie within the span of the data and can alternatively be understood in terms of a variant of dynamic mode decomposition. To validate our approach, we apply it to the complex Ginzburg-Landau equation and assess its robustness to measurement and process noise within the data. Finally, we demonstrate its practical utility by using it to study spatial transient growth in a transitional boundary layer.