It is known that the disintegration of vertical liquid curtains (sheets) is affected crucially by the amplification of free edge holes forming inside the curtain. This paper aims to investigate the influence of the hole expansion dynamics, driven by the so-called rim retraction, on the breakup of a liquid curtain, in both supercritical (Weber number $We > 1$) and subcritical ($We < 1$) conditions. The analysis is based on three-dimensional direct numerical simulations. For a selected supercritical configuration, the steady flow topology is first analysed. The investigation reveals the classic triangular shape regime of the steady curtain, due to the surface-tension-induced borders retraction towards its centre plane. The unsteady dynamics is then investigated as the curtain response to a hole perturbation introduced artificially in the steady flow configuration. The hole evolution determines a rim retraction phenomenon inside the curtain, which is influenced by both capillary and gravity forces. In supercritical conditions, the hole does not influence the curtain flow dynamics in the long-time limit. By reducing the Weber number slightly under the critical threshold ($We=1$), the initial amplification rate of the hole area increases, due to the stronger retraction effect of surface tension acting on the hole rims. The free hole expansion in fully subcritical conditions ($We < 1$) is investigated finally by simulating an edge-free curtain flow. As $We$ decreases progressively, the hole expands while it is convected downstream by gravity acceleration. In the range $0.4< We<1$, the subcritical curtain returns to the intact unperturbed configuration after the hole expulsion at the downstream outflow. For $We<0.4$, the surface tension force becomes strong enough to reverse the gravitational motion of the hole top point, which retracts upstream towards the sheet inlet section while expanding along the lateral directions. This last phenomenon causes finally the breakup of the curtain, which results in a columnar regime strictly resembling similar experimental findings of the literature.

Steady shock reflection where the incident shock is free of interaction with other waves has been well studied. In this paper, we consider the less studied shock reflection problem where the incident shock interacts with the wedge trailing-edge expansion fan, which occurs when the wedge trailing-edge height surpasses a threshold. The influence of this interaction on the advance of transition from Mach reflection to regular reflection is quantified in terms of the wedge trailing-edge height ratio. The wave pattern, including primary and reflected Mach waves, for Mach reflection with interaction is clarified using computational fluid dynamics (CFD) and the method of characteristics. Those reflected Mach waves having an important effect on Mach reflection are identified. A simplified Mach stem model that accounts for the direct role of the interaction on the incident shock and its indirect role on the reflected shock and slipline is built up on a past model without interaction. Both theory and CFD show that the Mach stem height decreases nonlinearly with increasing trailing-edge height.

With the severity and frequency of significant weather events increasing, methods for alleviating unsteady wind loading for high-rise buildings are gaining interest. This study numerically investigates the three-dimensional flow structures around a canonical high-rise building immersed in an atmospheric boundary layer at different oncoming wind angles, using wall-resolved large eddy simulations. A synthetic jet located on the top surface is used as open-loop active actuation with the aim of suppressing the building's side-force fluctuations when exposed to oncoming wind variations. Three different frequencies of jet forcing are considered, all half an order of magnitude larger than the vortex shedding frequency. The behaviour of the synthetic jet and its effect on the building's unsteady side force, time-averaged flow fields and unsteady flow structures are investigated numerically. The synthetic jet actuation is found to reduce the side-force fluctuation of the building, enhance the downwash flow and successfully attenuate the antisymmetric vortex shedding. This was achieved to different extents across the range of oncoming wind angles considered and may motivate future attempts to explore experimental active control strategies for attenuation of unsteady wind loading.