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.

中文翻译：

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湍流伴随的稳定化

对于湍流混沌流，传统的伴随变量呈指数增长。大多数提议的方法（例如，集合伴生，基于阴影的方法和基于不稳定子空间的方法等）在计算上都无法解决实际问题。在当前的论文中，我们评估了湍流伴随的稳定方法，与前面提到的方法相比，该方法在计算上便宜。稳定方法是通过研究伴随能量预算来实现的。然后将当前方法的结果伴随和参数灵敏度与最小流量单位的影子伴随方法进行比较。