Correction: An optimization framework for analyzing nonlinear stability due to sparse finite-amplitude perturbations

In this paper, we present an optimization framework for computing sparse and spatially-localized finite-amplitude perturbations that maximize transient growth in nonlinear systems. A variational approach is used to derive the first-order necessary conditions for optimality, which form the basis of our iterative direct-adjoint looping numerical solution algorithm. The method is demonstrated on an illustrative 2-state dynamical system that possesses key features of the incompressible Navier-Stokes equations. We then apply the method to analyze a reduced-order model of a sinusoidal shear flow at 𝑅𝑒 = 20 . Our results establish the power of the proposed optimization framework for revealing dominant modal interactions and sparse perturbation mechanisms for transient growth and instability in fluid flows.