The rapid development of high-performance computing has enabled the optimisation of turbulent flows using scale-resolving simulations (LES and DNS), thus bypassing current RANS-based approaches that have inherent limitations (such as accuracy). An objective function is defined (for example time-average lift or drag coefficient) that is optimised with respect to several control parameters. The optimisation is performed iteratively. At each iteration, the gradient of the objective function is computed using the adjoint method, and the control parameters are updated. The adjoint equations (obtained by linearising the governing equations along the trajectory) are marched backward in time. In turbulent flows, however, the adjoint variables grow exponentially during the backward integration step due to the so-called "butterfly effect". The least-squares shadowing method [1,2] is one of the most promising algorithms to deal with this problem. The method formulates and solves a separate optimisation problem and is capable of providing reliable sensitivity gradients. However, its computational cost increases rapidly with the number of its unstable modes and this limits its applicability to highly turbulent flows due to the rapid growth of the number of Lyapunov exponents with respect to the Reynolds number. To address this problem, we introduce a novel shadowing method that employs an augmented system with fewer number of positive Lyapunov exponents. The method is based on adding a control term that suppresses only the high frequencies, leaving low frequencies unaffected (this corresponds to a low pass filter, which is implemented in the time domain). The effectiveness of the proposed algorithm is tested in the Kuramoto-Sivashinsky system and the Kolmogorov flow. A comparison with the standard NILSS method [1] demonstrates the accuracy, stability, and reduced computational cost of the new method. The successful application of the algorithm in different scenarios makes it a valuable tool for large-scale three-dimensional complex turbulence control and optimisation studies. REFERENCES [1] A. Ni, Q. Wang, Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS), Journal of Computational Physics, Vol. 347, pp.56–77, 2017. [2] K D. Kantarakias, G. Papadakis, Sensitivity analysis of chaotic systems using a frequency-domain shadowing approach, Journal of Computational Physics, Vol. 474, 111757, 2023.