Stabilization of the Adjoint for Turbulent Flows

Traditional adjoint variables grow exponentially for turbulent chaotic flows. Most proposed methods (for example. ensemble adjoint, shadow-based, and unstable-subspace-based approaches, etc.) are computationally prohibitive for practical problems. In the current paper, we evaluate a stabilization approach for the adjoints of turbulent flows, which is computationally cheap compared to the previously mentioned methods. The stabilization method is motivated by studying the adjoint-energy budget. The resulting adjoint and the parameter sensitivity from the current approach are then compared with the shadow adjoint approach for the minimal flow unit.