Flame–wall interaction (FWI) of lean premixed hydrogen/air flames is critical in wall-bounded combustors, where thermodiffusive instabilities strongly influence quenching. To capture these effects efficiently in realistic configurations, reduced-order combustion models such as flamelet tabulation are desirable, as they lower resolution requirements and computational cost. In this study, advanced flamelet manifolds incorporating a mixture-averaged species diffusion model and thermal diffusion are developed to represent the FWI of thermodiffusively unstable lean hydrogen/air flames. A central challenge is the simultaneous capture of intrinsic instabilities and heat losses, each complex in itself. Separate manifolds addressing these effects are first introduced, providing the foundation for joint manifolds that capture both simultaneously. In this context, the choice of flamelet databases is examined by comparing freely propagating flames with exhaust gas recirculation, commonly used in flamelet modelling to represent enthalpy variations, with one-dimensional head-on quenching (HOQ) flames, which are essential for accurate prediction of wall heat flux and pollutant formation in hydrocarbon flames. The models are evaluated through both a-priori and a-posteriori analyses across increasingly complex configurations, culminating in the HOQ of a thermodiffusively unstable flame, where both instability and quenching must be captured simultaneously. Results show excellent agreement with reference simulations using detailed chemistry, accurately reproducing key features of the flame front, thermochemical state and global flame properties such as consumption speed and quenching wall heat flux. This marks a key advance in modelling hydrogen combustion and provides a robust foundation for studying safety-critical phenomena such as flame flashback linked to near-wall flame propagation.

Reconstructing near-wall turbulence from wall-based measurements is a critical yet inherently ill-posed problem in wall-bounded flows, where limited sensing and spatially heterogeneous flow–wall coupling challenge deterministic estimation strategies. To address this, we introduce a novel generative modelling framework based on conditional flow matching for synthesising instantaneous velocity fluctuation fields from wall observations, with explicit quantification of predictive uncertainty. Our method integrates continuous-time flow matching with a probabilistic forward operator trained using stochastic weight-averaging Gaussian, enabling zero-shot conditional generation without model re-training. We demonstrate that the proposed approach not only recovers physically realistic, statistically consistent turbulence structures across the near-wall region but also effectively adapts to various sensor configurations, including sparse, incomplete and low-resolution wall measurements. The model achieves robust uncertainty-aware reconstruction, preserving flow intermittency and structure even under significantly degraded observability. Compared with classical linear stochastic estimation and deterministic convolutional neural network methods, our stochastic generative learning framework exhibits superior generalisation for unseen realisations under same flow conditions and resilience under measurement sparsity with quantified uncertainty. This work establishes a robust semi-supervised generative modelling paradigm for data-consistent flow reconstruction and lays the foundation for uncertainty-aware, sensor-driven modelling of wall-bounded turbulence.

In this study, experimental deep reinforcement learning (DRL) control of a supersonic cavity flow is conducted for the first time at Mach 2, with the aim of mixing enhancement. A 4 $\times$ 5 pulsed-arc plasma actuator (PAPA) matrix with independently controlled columns and a supersonic hot-wire probe placed at the cavity midline serve as the flow disturber and state observer, respectively. The control law parametrised by a radial basis function network is executed on a field-programmable gate array at 5 kHz loop frequency. Results show that DRL is capable of finding a converged closed-loop control law in less than 10 s, and the resulting cavity velocity fluctuation is three times higher than periodic open-loop control. The control benefits earned by DRL increase with the number of activated columns, yet reduce with the cavity back-wall inclination angle. Using the same number of actuator columns, variable-formation actuation mode allows the DRL to find a more effective control with much less actuator power consumption, when compared with fixed-formation actuation mode. The final control law obtained by DRL can be interpreted as a threshold control conditional on the location of the state vector, and the improvement of total reward is ascribed to both the elevation of occurrence probabilities of high-reward clusters and the ubiquitous increase of the reward expectation at each cluster. Physically, mixing enhancement in the cavity flow is traced back to the thermal bulbs and shock waves produced by the PAPA, which induce a meandering motion of the shear layer.

Direct numerical simulation (DNS) of temporally developing natural convection boundary layers is conducted at $ \textit{Pr} =4.16$ and $ \textit{Pr} =6$. Results are compared with an existing DNS dataset for $ \textit{Pr} =0.71$ (Ke et al. J. Fluid Mech. 964, 2023, p. A24) to enable a direct assessment of Prandtl number effects across the range $0.71\leqslant \textit{Pr} \leqslant 6$. The analysis reveals that the $ \textit{Pr}$ affects the flow through buoyancy forcing, which acts not only as the driving force but also modulates the local shear distribution via coupling with the momentum equation, thereby shifting the onset Rayleigh number of transition from the laminar regime. This transition is found to be characterised by the thermal boundary layer thickness $\delta _\theta$, which provides a robust prediction of the critical Rayleigh number across $ \textit{Pr}$, indicating a buoyancy instability consistent with the stability analysis (Ke et al. J. Fluid Mech. 988, 2024, p. A44; Ke et al. Intl J. Heat Mass Transfer 241, 2025, p. 126670). Further analysis in the turbulent regime suggests that while heat transfer becomes effectively independent of $ \textit{Pr}$, the near-wall turbulence structure remains sensitive to $ \textit{Pr}$ due to persistent buoyancy effects. The skin friction coefficient scaling shows clear transition from a linear scaling with the bulk Reynolds number in the weakly turbulent regime to a log-law-type scaling with the bulk Reynolds number in the ultimate turbulent regime (Grossmann & Lohse J. Fluid Mech. 407, 2000, pp. 27–56). The premultiplied velocity spectra confirms the development of near-wall streaks that are characteristic of canonical shear-driven turbulence in this ultimate turbulent regime, with their spanwise spacing systematically broadening with increasing $ \textit{Pr}$ due to persistent buoyancy effects; while the spectral signature of the outer plume-like region appears largely $ \textit{Pr}$-independent.