Gradient-free learning of a closed-loop wall controller for turbulent drag reduction

• URL: http://arxiv.org/abs/2607.12626v1
• Date: Tue, 14 Jul 2026 11:04:11 GMT
• Title: Gradient-free learning of a closed-loop wall controller for turbulent drag reduction
• Abstract summary: We employ Evolution Strategy (ES) to optimise a recurrent closed-loop controller on a turbulent channel at $mathitRe_simeq180$.<n>The ES controller reduces the skin friction by about $26%$, exceeding the gradient-based multi-agent controller of Cavallazzi et al. (2026), GRU-MARL, trained on a minimal box ($17%$), and marginally exceeding classic opposition control (OC, $22%$)<n>A wall-normal decomposition of the friction, Reynolds-stress profiles and anisotropy invariants show that the ES
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Closed-loop wall control learnt by multi-agent reinforcement learning can lower skin-friction drag in turbulent channels, but these gradient-based policies are trained on small periodic boxes and exhibit reduced performance when carried over to a larger domain. We recently showed that such policies are also prone to saturated bang-bang actuations that collapse into standing streamwise waves whose scale is set by the computational box rather than by the near-wall cycle, and proposed architectural fixes that avoid these degeneracies. Here, we employ Evolution Strategy (ES) to optimise a recurrent closed-loop controller directly on a large turbulent channel at $\mathit{Re}_τ\simeq180$, evaluating policy performance over full flow episodes using an energy-aware criterion and processing candidate policies in parallel. To our knowledge, this is the first application of an evolution strategy to the control of a turbulent flow. The ES controller reduces the skin friction by about $26\%$, exceeding the gradient-based multi-agent controller of Cavallazzi et al. (2026), GRU-MARL, trained on a minimal box ($17\%$), and marginally exceeding classic opposition control (OC, $22\%$). A wall-normal decomposition of the friction, Reynolds-stress profiles and anisotropy invariants show that the ES and opposition-controlled flows follow separate trajectories through the buffer layer, reaching comparable drag reduction by different reorganisations of the near-wall turbulence. In particular, the ES actuation correlates predominantly with the streamwise velocity fluctuations rather than with the wall-normal velocity that classical OC targets.

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