Hypersonic flow over a two-dimensional compression corner is investigated using computational fluid dynamics and global resolvent analysis in this study, which is a continuation of the work done by Hao et al. (J. Fluid Mech., vol. 919, 2021, p. A4). The same baseline free-stream conditions with a Mach number of 7.7 and a unit Reynolds number of 4.2 × 106 m−1 are considered. The ramp angles range from 0° (equivalent to a flat plate) to 12° (slightly below the critical angle of global instability). During this process, the base flow evolves from no separation to incipient separation to large separation. The resolvent analysis reveals that the optimal response to upstream disturbances localised near the leading edge is in the form of steady streamwise streaks for all interaction strengths, which arise from transient growth in the flat-plate boundary layer due to the lift-up mechanism and significantly grow near the corner due to the Görtler instability. The most amplified spanwise wavelength decreases as the ramp angle is increased and scales with the incoming boundary-layer thickness.

Flow and turbulent structures generated by the interaction of forced incoming oscillatory flow with a circular, vertical cylinder placed in an open channel with a horizontal bed are investigated using eddy-resolving simulations. Validation simulations performed with a Keulegan–Carpenter (KC) number of 20 and multiple-mode forcing corresponding to the laboratory experiment of Sumer et al. (J. Fluid Mech., vol. 332, 1997, pp. 41–70) show that detached eddy simulation (DES) predicts more accurately the amplification of the bed shear stress beneath the horseshoe vortex system (upstream side of the cylinder) and the maximum magnitude of the bed shear stress at the downstream (wake) side of the cylinder compared with unsteady Reynolds-averaged Navier–Stokes simulations. High-Reynolds-number DES simulations are then conducted with 1.5 ≤ KC ≤ 30.8 and one-mode sinusoidal forcing of the streamwise velocity in the approaching flow to investigate the changes in the wake vortex-flow regimes, the coherence of the horseshoe vortices and the generation of other near-bed coherent structures in the wake during the oscillatory cycle. The flow is periodic, no horseshoe vortices form and no vortices are shed in the wake for KC = 1.5. By contrast, for KC ≥ 8 horseshoe vortices are present over part of the oscillatory cycle and up to three wake vortices are shed over each half-cycle as KC is increased to 30.8. For an intermediate range of KC numbers, one (KC = 15.4) or two (KC = 8) of the vortices forming at the back of the cylinder during each half-cycle are washed around it when the flow reverses. The main horseshoe vortex and other horizontal near-bed vortices have a large capacity to amplify the bed shear stresses when the incoming velocity magnitude is significantly less than its peak value. Assuming the depth-averaged velocity in the incoming (undisturbed) oscillatory flow is the same in simulations conducted with different KC numbers, the peak values of the sediment entrainment potential measured by the mean (cycle-averaged) volumetric flux of sediment entrained from the bed over one oscillatory cycle occur for 8 ≤ KC ≤ 15.4. For all KC numbers, the in-line force variation over the oscillatory cycle is fairly well approximated by the Morison equation. For KC = 1.5, the in-line force is only due to inertia effects. For KC = 30.8, the maximum and minimum values of the phase-averaged in-line force are approximatively in phase with those of the incoming flow velocity. For KC ≥ 15, the phase-averaged in-line force coefficients vary between 0.8 and 1.1 during most of the oscillatory cycle (e.g. when the incoming flow velocity is not close to zero). This is different from cases with KC ≤ 8 where the in-line force coefficient is equal to zero twice during the oscillatory cycle as the in-line force becomes equal to zero for non-zero values of the incoming velocity. The largest cycle-to-cycle variations of the in-line force coefficient and in-line force are observed around KC = 8. For KC = 8 and 15.4, the cylinder is subject to relatively large phase-averaged spanwise drag forces that are comparable to the peak phase-averaged streamwise drag forces. As KC is increased to 30.8, the phase-averaged spanwise drag force becomes zero over the whole oscillatory cycle but the cylinder is still subject to large instantaneous spanwise forces over part of the oscillatory cycle.

Due to the curvature of the droplet surface, the propagation of transmitted waves is complex inside a droplet impacted by an incident shock wave. The wave converging phenomena inside a two-dimensional water column impacted by different curved shock waves are explored in this paper by means of theoretical ray analysis and high-resolution numerical simulations. An analytical method describing the wave structure evolution characteristics inside the shocked water column is established. Hence, the morphological pattern and focus locations of these waves are theoretically obtained. The analysis shows that both the first and the second reflected waves focus inside the water column regardless of the convergent, planar or divergent nature of the incident shock wave shape. The dimensionless distances from focusing points to the column centre are derived as ${\kappa }/{( 3\kappa -{{M}_{0}}{{f}_{s}} )}$ for the former and ${\kappa }/{( 5\kappa -{{M}_{0}}{{f}_{s}})}$ for the latter, respectively. Here, $\kappa$, $M_0$ and $f_s$ represent the sound-speed ratio of the two phases, the incident shock wave strength and a function characterising the shock wave shape effect, respectively. Moreover, highly negative pressures due to the first reflected wave focusing and significant pressure oscillations due to the second reflected wave focusing are numerically tracked for three shapes of the incident shock. The effects of the incident shock wave intensity on the pressure variations at focus points are further studied. As the incident shock wave intensity increases, stronger negative pressure and higher pressure oscillation are induced. The converged incident shock wave can enhance the above phenomena, but the diverged one can weaken them.

The suborder Phacopina, characterized by schizochroal eyes, is among the most common groups of trilobites in Devonian strata. The marine sediments of the Famennian in western Junggar, Xinjiang, contain abundant low-disparity phacopids, which have previously been designated to Omegops accipitrinus mobilis, Phacops circumspectans tuberculosus, and Omegops cornelius on the basis of small numbers of poorly preserved specimens. In this study, these phacopids were identified as two new species of Omegops, O. honggulelengensis n. sp. and O. xiangi n. sp., on the basis of nearly 200 well-preserved specimens. The intraspecific variations of eye lenses of these specimens were quantitatively analyzed. On the basis of differences in the total number, number of dorsoventral files, and arrangement of the eye lenses, the absence of lenses in the middle part of the visual surface, and asymmetry of the number and/or arrangement of lenses in the two eyes, it was concluded that the reasons for intraspecific variation in eye lenses of Late Devonian Omegops from western Junggar were different from previously described factors but were likely genetic or embryological malfunctions or abnormalities caused by pathological conditions. Diversity of lenses in the schizochroal eyes shows that the number and arrangement of eye lenses was not stable in Phacopina. Therefore, many specimens are needed for quantitative study to determine the true characteristics of the number or arrangement of eye lenses when these features are used in the systematic taxonomy of Phacopina.

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Shock-tube experiments are performed on the convergent Richtmyer–Meshkov (RM) instability of a multimode interface. The temporal growth of each Fourier mode perturbation is measured. The hydrodynamic instabilities, including the RM instability and the additional Rayleigh–Taylor (RT) effect, imposed by the convergent shock wave on the dual-mode interface, are investigated. The mode-coupling effect on the convergent RM instability coupled with the RT effect is quantified. It is evident that the amplitude growths of all first-order modes and second-order harmonics and their couplings depend on the variance of the interface radius, and are influenced by the mode-coupling from the very beginning. It is confirmed that the mode-coupling mechanism is closely related to the initial spectrum, including azimuthal wavenumbers, relative phases and initial amplitudes of the constituent modes. Different from the conclusion in previous studies on the convergent single-mode RM instability that the additional RT effect always suppresses the perturbation growth, the mode-coupling might result in the additional RT effect promoting the instability of the constituent Fourier mode. By considering the geometry convergence, the mode-coupling effect and other physical mechanisms, second-order nonlinear solutions are established to predict the RM instability and the additional RT effect in the cylindrical geometry, reasonably quantifying the amplitude growths of each mode, harmonic and coupling. The nonlinear solutions are further validated by simulations considering various initial spectra. Last, the temporal evolutions of the mixed mass and normalized mixed mass of a shocked multimode interface are calculated numerically to quantify the mixing of two fluids in the cylindrical geometry.

This article examines the different mechanisms of the circulation of Chinese ceramics in the Middle East during the Abbasid-Chinese ceramic exchange during the eighth–tenth centuries ce. Although trade has been used conveniently to denote the circulation of Chinese wares in the Abbasid Caliphate, it is not the only mechanism that existed. There were also other possible processes of circulation, such as ceramics sent as tributes, diplomatic gifts, and samples, and secondary distribution through looting and pilgrimage. Not all Chinese wares shipped to the Middle East were luxury goods. Different types of Chinese wares had different functions and commercial and aesthetic values in the Middle East. It is an oversimplification to describe the circulation of Chinese wares in the Middle East as merely the result of the luxury goods trade.

Mechanical metamaterials have attracted extensive attention. This paper reports a metamaterial with tunable elastic wave bandgaps based on bistable buckling structure. First, we find that deformation of two symmetric buckling shells is intrinsically asymmetric, which blocks the realisation of robust tunability. Based on an analytical model, we clarify that the mechanisms for this intrinsic asymmetricity are the bifurcations on force–deformation curves. Then we propose a superposition method of buckling shells, which can realise the symmetric deformation for robust tunable stiffness. Using this variable-stiffness oscillator, we design a metamaterial sandwich beam, and numerically and experimentally demonstrate its tunable bandgap for vibration suppression. This paper presents the unusual deformation process of buckling elements widely used for constructing metamaterials, and provides a robust way to realise metamaterials with tunable vibration bandgaps.

In this paper, we reduce the logarithmic Sarnak conjecture to the $\{0,1\}$ -symbolic systems with polynomial mean complexity. By showing that the logarithmic Sarnak conjecture holds for any topologically dynamical system with sublinear complexity, we provide a variant of the $1$ -Fourier uniformity conjecture, where the frequencies are restricted to any subset of $[0,1]$ with packing dimension less than one.