Policy-based optimisation of spanwise wall oscillation waveforms for dissimilar-heat-transfer enhancement

The application of spanwise wall oscillations (SWO) to turbulent flow control has been largely confined to sinusoidal forcing and drag-reduction objectives; the optimisation of waveform topology across a continuous parameter space, and the application of SWO to dissimilar heat transfer (DHT), wherein the analogy factor Aₙ quantifies the ratio of thermal to drag enhancement, remain unexplored. A policy-based optimisation framework coupled with implicit large-eddy simulations and Lagrangian-polynomial waveform parameterisation is employed to investigate four optimisation problems at Re_τ = 200 and Pr = 1 , where $Re$ is the friction Reynolds number and $Pr$ is the Prandtl number. Drag-reduction benchmarks validate the framework and establish that non-sinusoidal waveforms lead to no advantage for net energetic gain, whilst recovering a quasi-plateau topology that outperforms sinusoidal forcing when drag savings alone are maximised. Applied to DHT, waveform optimisation at 25 % reduced amplitude identifies a quasi-plateau configuration that achieves Aₙ̄ = 1.087 , matching the sinusoidal optimum ( Aₙ̄ = 1.091 ) whilst employing 7.4 % less control energy and producing 37.9 % greater absolute heat-transfer enhancement. These gains establish that sustained Stokes-layer strain during plateau phases governs preferential thermal transport through mechanisms fundamentally distinct from drag reduction. Phase-resolved analysis of the variance modulation reveals that the temperature variance regenerates more effectively and over a broader temporal interval than the velocity variance during the lingering phases, whilst the velocity field is suppressed earlier at the strain reversal. This asymmetric regeneration, hypothesised to originate in the pressure-strain redistribution term present exclusively in the momentum equations, constitutes the phase-resolved fingerprint of Reynolds analogy breaking even at Pr = 1 . Waveform optimisation is thereby established as a superior, energy-efficient alternative to amplitude escalation for thermal management applications such as concentrated solar power receivers.