Feasibility Analysis of Ensemble Sensitivity Computation in Turbulent Flows

Abstract

© 2019 by the American Institute of Aeronautics and Astronautics, Inc. In chaotic systems, such as turbulent flows, the solutions to tangent and adjoint equations exhibit an unbounded growth in their norms. This behavior renders the instantaneous tangent and adjoint solutions unusable for sensitivity analysis. The Lea-Allen-Haine ensemble sensitivity (ES) estimates provide a way of computing meaningful sensitivities in chaotic systems by using tangent/adjoint solutions over short trajectories. In this paper, the feasibility of ES computations is analyzed under optimistic mathematical assumptions on the flow dynamics. Furthermore, upper bounds are estimated on the rate of convergence of the ES method in numerical simulations of turbulent flow. Even at the optimistic upper bound, the ES method is computationally intractable in each of the numerical examples considered.