This study implements blowing/suction control for aerofoil trailing-edge noise and systematically optimises blowing/suction angles and control locations within a Bayesian framework. Two distinct rounds were conducted for direct and sound-source-oriented coarse-grained Bayesian optimisations. In the direct optimisation, the mean overall sound pressure level of far-field noise is selected as the objective function. Optimal control parameters were obtained after 15 iterations, requiring 80 three-dimensional implicit large eddy simulations, and achieved a noise reduction of up to 3.7 dB. To reduce the substantial computational cost, a Gaussian process surrogate model was constructed using the sound source defined by multi-process acoustic theory. This enabled a second round of optimisation, termed sound-source-oriented coarse-grained Bayesian optimisation, which yielded comparable noise reduction. This refined approach exhibited low signal delay and rapid statistical convergence, which can significantly reduce both the computational cost per sampling and the iteration number. Consequently, the total computational cost was reduced to approximately one-sixth of the initial direct optimisation. Moreover, physical insights into noise reduction mechanisms were elucidated through dynamic mode decomposition (DMD), anisotropic invariant mapping and the analysis of source terms within the TNO model across several typical cases. The results indicate that the blowing-control case induces large-scale vortex shedding and enhances DMD mode energy and low-frequency noise emission. Furthermore, the suction control tends to disrupt coherent structures, reduce DMD mode energy and suppress radiated noise. Crucially, the suction control significantly decreases mean velocity gradients within the logarithmic layer and suppresses wall-normal Reynolds stresses, thereby considerably reducing TNO source intensity in this critical region. The optimal case exhibits superior performance across all metrics above, thus laying the foundation for the optimal control strategy. Additionally, the suction control facilitates attenuating the footprint of turbulent motions in wall-pressure fluctuations through pressure-velocity coherence analysis, hence promoting noise reduction. This work introduces a novel framework that integrates Bayesian optimisation with advanced noise diagnostic theory, and provides actionable insights for effective trailing-edge noise mitigation.

The Earth’s quasi-biennial oscillation (QBO) is a natural example of wave–mean flow interaction and corresponds to the alternating directions of winds in the equatorial stratosphere. It is due to internal gravity waves (IGWs) generated in the underlying convective troposphere. In stars, a similar situation is predicted to occur, with the interaction of a stably stratified radiative zone and a convective zone. In this context, we investigate the dynamics of this reversing mean flow by modelling a stably stratified envelope and a convectively unstable core in polar geometry. Here, the coupling between the two zones is achieved self-consistently, and IGWs generated through convection lead to the formation of a reversing azimuthal mean flow in the upper layer. We characterise the mean flow oscillations by their periods, velocity amplitudes and regularity. Despite a continuous broad spectrum of IGWs, our work shows good qualitative agreement with the monochromatic model of Plumb & McEwan (1978, J. Atmos. Sci. vol. 35, no. 10, pp. 1827–1839). While the latter was originally developed in the context of the Earth’s QBO, then our study could prove relevant for its stellar counterpart in massive stars, which host convective cores and radiative envelopes.

A combined experimental and numerical investigation was conducted to examine the mechanisms of aerodynamic noise reduction for twisted hexagonal cylinders at Reynolds numbers ($ \textit{Re} = 2\times 10^4$–$10^5$) and twist angles per unit span $\gamma ^*\in \mathbb{R}[0,1/3]$. It reveals a non-monotonic dependence of noise reduction on $\gamma ^*$, optimised for $\gamma ^* = 1/6$, where a tonal noise reduction of 15 dB and a total sound reduction of 11 dB at $ \textit{Re} = 2\times 10^4$ were achieved. This was consistent across all Reynolds numbers tested. Additionally, dual tones were observed in the noise spectra for cases with $1/18\leqslant \gamma ^* \lt 1/6$, leading to the identification of two distinct flow patterns (Pattern I and II) based on the number of tones in the spectrum. Large-eddy simulations were performed at $ \textit{Re} = 2\times 10^4$ to support the acoustic measurements. Spanwise variations in flow separation gave rise to two distinct regimes: separation (RI) and reattachment (RII). For Pattern I ($1/5.4 \leqslant \gamma ^* \leqslant 1/3$), the spanwise variation of shear layer separation induced wavy vortex shedding, contributing to a moderate noise reduction. For Pattern II ($1/18 \leqslant \gamma ^* \leqslant 1/7.2$), differences in vortex shedding frequencies between RI and RII regimes led to vortex dislocation, forming C- or X-type vortex structures. The $\gamma ^* = 1/6$ configuration leads to a transitional pattern between Pattern I and II, where modulation was predominantly observed in the RI regime. The superior noise reduction of $\gamma ^* = 1/6$ stems from the combined effects of frequent vortex dislocation and modulation, which reduces spanwise coherency and increases wake three-dimensionality.

This study investigates the heat-flux enhancement of convection flows inside a fluid layer bounded from the top and bottom by two inhomogeneous porous layers. The porous matrix is made of solid materials with very high diffusivity. The numerical results reveal that, compared with the traditional convection system, the heat flux is greatly increased when the thickness of porous layer is large enough. At small Rayleigh numbers, the enhancement is the result of the increase in effective diffusivity in the fluid-saturated porous layers and the reduction in flow friction at the porous interface. For large Rayleigh numbers, the permeable motions across the interfaces generate strong convective flux, which greatly increases the total heat flux. For the latter parameter range, the exponent of the power-law scaling between the Nusselt number and the Rayleigh number exceeds 1/2, which is the value of the ultimate scaling. Our findings are not only of great potential in heat management in various industrial applications but also imply that, in many natural systems with imperfect boundaries, the global heat flux may be much stronger than the prediction by using a convection system with perfect boundaries.

This paper explores dispersive shock waves (DSWs) of gravity-capillary waves within the framework of the two-dimensional, fully nonlinear Euler equations. In this system, initial wave profiles characterised by a smooth step function evolve into modulated wavetrains that connect different constant states, a phenomenon arising from the interplay between nonlinear and dispersive effects. The Bond number, which quantifies the relative significance of gravity compared to surface tension, is crucial in determining the behaviour of the DSW solution. As the Bond number increases from zero, solutions traverse four distinct zones: the radiating DSW region, an unstable crossover region, the travelling DSW region, and the inverse radiating DSW region. The propagation velocities of DSWs can be estimated using the DSW fitting method alongside numerical results from travelling waves. Particular attention is given to travelling DSWs, which are characterised by a uniform wavetrain followed by an oscillatory decaying wavepacket. Notably, the high platform and its extended periodic wavetrain can be part of a specific type of gravity-capillary solitary wave that features an oscillatory pulse, with the number of oscillations at the core potentially increasing indefinitely. The Whitham modulation theory for the Euler equations is employed to describe the modulation parameters – such as wavenumber, amplitude and wave mean – in the travelling DSW region. Finally, we discuss the bifurcation mechanism of solitary waves with oscillatory pulses in the Euler equations, along with analyses of their stability. It is also demonstrated that for relatively small Bond numbers, a series of trapped bubbles can occur along the bifurcation curves, representing the limiting configuration of this type of solitary wave.