Six types of shock wave interference resulting from the impingement of an incident shock on a bow shock are revisited by examining the sub-types that arise between the canonical types. Several new sub-types are predicted based on the theories of weak shock reflection and double-wedge shock interference, and verified via numerical simulations. Two additional types, Type IIw and Type IIs, are identified between Type II and Type III, whereas a Type Vw emerges between Type IV and Type V. These types originate from the transformation of the Mach reflection at the triple point, which evolves through weak shock reflections (von Neumann reflection, Vasilev reflection, Guderley reflection) before disappearing. The transition from Type III to Type IV is further shown to mirror sequences of double-wedge shock interference. Two additional types (Type IIIb and Type IVt) are found. Meanwhile, it is found that under large incoming flow Mach number ($M_0$ = 5), Types III, IV and their sub-types dominate, whereas Type II is absent; under small incoming flow Mach number ($M_0$ = 2.5), Types III and IV vanish and a modified Type Va emerges. This study adds seven new sub-types to the existing six types of shock interference. These work extend the classical six types of shock interferences into six-plus shock interference, a picture that shed new insight into shock interference.

Direct numerical simulations with two-way coupled Lagrangian tracking are carried out to study the bubble preferential concentration and the flow field modification. Simulations are conducted in an upward vertical turbulent channel driven by a constant pressure gradient, corresponding to a friction Reynolds number $Re_{\tau 0}=180$. Micro-sized bubbles with diameters ranging from 0.72 to 1.43 wall units are considered. Competition between lift force and wall-lift force in the wall-normal direction leads to significant near-wall bubble accumulation and directly results in distinct preferential concentration patterns across the channel. Below (above) the peak concentration height, the wall-lift (lift) force dominates, driving bubbles to accumulate in regions of high-speed sweep (low-speed ejection) events. In the vicinity of the wall, the wall-normal lift force exhibits a strong correlation with the local streamwise flow velocity, further reinforcing the preferential concentration of bubbles in high-speed regions. Additionally, bubbles show a strong preference for the low-enstrophy and high-dissipation nodal topologies. Furthermore, small bubbles primarily accumulate in the vicinity of the wall, reducing the work done on the flow and leading to a decrease in bulk velocity and turbulence statistics. In contrast, the turbulence statistics of large bubbles are nearly identical to those of the unladen flow. The impact of large bubbles on the flow field primarily manifests as an effective increase in the mean pressure gradient. These findings demonstrate that bubbles in the upward vertical channel flow exhibit strong preferential concentration behaviours, whereas their ability to modulate turbulence remains limited.

An oscillating body floating at the water surface produces a field of self-generated waves. When the oscillation induces a difference in fore–aft wave amplitude squared, these self-generated waves can be used as a mechanism to propel the body horizontally across the surface (Longuet-Higgins 1977 Proc. R. Soc. Lond. A, vol. 352, no. 1671, pp. 463–480). The optimisation of this wave-driven propulsion is the interest of this work. To study the conditions necessary to produce optimal thrust we will consider a shallow water set-up where a periodically oscillating pressure source acts as the body. In this framework, an expression for the thrust is derived by relation to the difference in fore–aft amplitude squared. The conditions on the source for maximal thrust are explored both analytically and numerically in two optimal control problems. The first case is where a bound is imposed on the norm of the control function to regularise it. Secondly, a more physically motivated case is studied where the power injected by the source is bounded. The body is permitted to have a drift velocity $U$. When scaled with the wave speed $c$, the dimensionless velocity $v=U/c$ divides the study into subcritical, critical and supercritical regimes and the optimal conditions are presented for each. The result in the bounded power case is then used to demonstrate how the modulation of power injected can slowly change the cruising velocity from rest to supercritical velocities.

In this study, direct numerical simulation of a turbulent flame–wall interaction (FWI) has been done for premixed H$_2/$air and NH$_3/$H$_2/$air flames in a fully developed channel flow at Re$_\tau$ $\approx$ 300. Both isothermal and adiabatic walls are considered. The results contribute to further clarification of the underlying mechanisms of FWIs. First, the underlying mechanism for the rapid increase of chemical flame thickness near the wall is found to be the zero-flux boundary condition for diffusion. Effects of wall heat loss and wall turbulence are minor. Then, a ridge-based flame surface identification method is proposed to track the flame front, which is found to be more accurate than an isosurface of $C$ (the progress variable), especially during FWIs. Using this technique, the near-wall flame geometry and orientation are correctly captured. It is found that the flames are laminarised near the wall and almost parallel to the isothermal wall shortly before quenching. Flame–vortex interactions lead to entrained flame pockets for H$_2$ as a fuel and to a distributed reaction zone for the case of NH$_3/$H$_2$. Finally, the turbulent combustion regime is investigated by checking wall-distance-dependent Reynolds number and Karlovitz number. It is found that the flames enter the laminar flame regime shortly before wall quenching, instead of the broken reaction regime suggested in previous studies. To support the analysis, the turbulent flame dynamics, including turbulent burning rate, turbulent flame surface area, flame stretch factor, local displacement speed, flame dilatation, flame strain rate (both tangential and normal) and flame alignment with the principal strain rate are quantified, providing a full picture of near-wall turbulent flames for the considered conditions.