We investigate the evolution of an external particle jet in a dense particle bed subjected to a radially divergent air-blast. Both random and single-mode perturbations are considered. By analysing the particle dynamics, we show that the Rayleigh–Taylor instability (RTI), the Richtmyer–Meshkov instability (RMI) and large particle inertia contribute to the formation of the external jet. The external particle jet exhibits a spike-like structure at its top and a bubble-like structure near its bottom. As the expanding particle bed lowers the internal gas pressure, particles near the bubble experience strong inward coupling forces and undergo RTI with variable acceleration. Meanwhile, particles in the spike experience weak gas–particle coupling and collision forces due to large particle inertia and low particle volume fraction, respectively. Consequently, the particles in the spike retain a nearly constant velocity, in contrast to the accelerating spikes observed in cylindrical RTI. To investigate the contributions of RMI to the particle jet growth, we track the trough-near particles in the single-mode perturbation case. It is revealed that the trough-near particles accelerate under the perturbation-induced pressure gradient, overtaking the crest-near particles and inducing phase inversion, thereby resulting in an increase in jet length. We establish a linear-growth model for the jet length increment, similar to the planar Richtmyer–Meshkov impulsive model. Combined with the jet-length-increment model, we propose an external-particle-jet-length model that is consistent with both numerical and experimental results for diverse initial gas pocket central pressures and particle bed thicknesses.

Asymptotic flow states with limiting drag modification are explored via direct numerical simulations in a moderate-curvature viscoelastic Taylor–Couette flow of the FENE-P fluid. We show that asymptotic drag modification (ADM) states are achieved at different solvent-to-total viscosity ratios ($\beta$) by gradually increasing the Weissenberg number from 10 to 150. As $\beta$ decreases from 0.99 to 0.90, for the first time, a continuous transition pathway is realised from the maximum drag reduction to the maximum drag enhancement, revealing a complete phase diagram of the ADM states. This transition originates from the competition between Reynolds stress reduction and polymer stress development, namely, a mechanistic change in angular momentum transport. Reduced $\beta$ has been found to effectively enhance elastic instability, suppressing large-scale Taylor vortices while promoting the formation of small-scale elastic Görtler vortices. The enhancement and in turn dominance of small-scale structures result in stronger incoherent transport, facilitating efficient mixing and substantial polymer stress development that ultimately drives the AMD state transition. Further analysis of the scale-decomposed transport equation of turbulent kinetic energy reveals an inverse energy cascade in the gap centre, which is attributed to the polymer-induced energy redistribution: polymers extract more energy from large scales than they can dissipate, with the excess energy redirected to smaller scales. However, the energy accumulating at smaller scales cannot be dissipated immediately and is consequently transferred back to larger scales via nonlinear interactions, thereby unravelling a novel polymer-mediated cycle for the reverse energy cascade. Overall, this study unravels the challenging puzzle of the existence of distinct dynamically connected ADM states and paves the way for coordinated experimental, simulation and theoretical studies of transition pathways to desired ADM states.

The guided-jet waves (GJWs) that may be trapped into a jet are investigated by simulating the propagation of the waves generated by an acoustic source on the axis of a jet at a Mach number of 0.95. The flow is modelled as a cylindrical shear layer to avoid reflections in the axial direction. For the source frequencies considered, GJWs belonging to the first two radial GJW axisymmetric modes are observed. They propagate in the upstream or downstream directions, and are entirely or partially contained in the flow, depending on the frequency. Their amplitudes are quantified. In the frequency–wavenumber space, they lie along the GJW dispersion curves predicted using linear-stability analysis. At specific spatial locations, they vary strongly and sharply with the frequency, exhibiting tonal-like peaks near the frequencies of the stationary points in the dispersion curves where the GJWs are standing waves with zero group velocity. Given the flow configuration, these properties can be attributed to propagation effects not requiring axial resonance between upstream- and downstream-travelling waves. Finally, it can be noted that, upstream of the source, outside the jet, the GJW amplitudes fluctuate in a reverse sawtooth manner with very intense peaks up to 30 dB higher than the levels obtained without flow at 10 jet radii from the source, similarly to the GJW footprints in the near-nozzle spectra of high-subsonic jets.

The growth of wall-mounted ice within channel flow which leads to a constriction is of significant practical relevance, especially in applications relating to aero-icing, large-scale pipe networks and mechanical systems. Whilst earlier works have treated ice constrictions as independent of the oncoming flow, few models explicitly account for the two-way coupling between the thermal and dynamical properties of the fluid and the evolving ice. To this end, the present work seeks to describe the interaction between high-Reynolds-number channel flow and constricting ice boundaries governed by Stefan conditions. Numerical simulations of the model indeed reveal that ice forming on the channel walls grows inwards towards the centreline and subsequently creates almost total constriction. In other parameter regimes, however, there is no ice formation. Using both a numerical and asymptotic approach, we identify regions of parameter space in which ice formation, and subsequently flow constriction, does or does not occur.