Shear instabilities at the interface of two fluids, such as classical Kelvin–Helmholtz instability (KHI), is the precursor of interface destabilization, leading to fluid fragmentation critical in a wide range of applications. While many insights into such instabilities are derived for steady background forcing flow, unsteady impulse flows are ubiquitous in environmental and physiological processes. Yet, little is understood on how unsteadiness shapes the initial interface amplification necessary for the onset of its topological change enabling subsequent fragmentation. In this combined theoretical, numerical and experimental study, we focus on an air-on-liquid interface exposed to canonical unsteady shear flow profiles. Evolution of the perturbed interface is formulated theoretically as an impulse-driven initial value problem using both linearized potential flow and nonlinear boundary integral methods. We show that the unsteady airflow forcing can amplify the interface's inherent gravity–capillary wave, up to wave-breaking transition, even if the configuration is classically KH stable. For impulses much shorter than the gravity–capillary wave period, it is the cumulative action, akin to total energy, that determines amplification, independent of the details of the impulse profile. However, for longer impulses, the details of the impulse profile become important. In this limit, akin to a resonance, it is the entangled history of the interaction of the forcing, i.e. the impulse, that changes rapidly in amplitude, and the response of the oscillating interface that matters. The insights gained are discussed and experimentally illustrated in the context of interface distortion and destabilization relevant for upper respiratory mucosalivary fluid fragmentation in violent exhalations.

We study the stability and collapse of holes at the wall in liquid layers on circular bounded containers with various wettabilities. Three distinct wetting modes of the hole are observed, which are related to the wettability of the container: when the substrate and the inner wall of the container are superhydrophobic, a stable hole remains as the liquid volume is continuously increased until the liquid layer covers the entire substrate; when the substrate and the inner wall are hydrophobic, an eye-shaped hole remains stable as the projected area of the hole exceeds a critical value $A_c$, however, the hole collapses if the liquid volume is further increased; when the substrate is superhydrophobic but the wall is hydrophilic, on increasing the liquid volume, the hole suddenly transfers into a circular hole and is pushed against the wall, leaving the hole dwelling around the centre of the container. Theoretical analyses and numerical simulations are conducted to establish the phase diagram for different wetting modes. It is found that, in the second mode, $A_c$ increases with the size of the container but decreases with the contact angle of the substrate and the wall. Furthermore, we experimentally investigate the dynamics of the hole. The time evolution of the area of the hole obeys a scaling relationship $A \sim (t_0 - t)^{1.1}$ after the hole collapses at time $t_0$.

This paper presents a vortex breakdown study due to the interaction between a Batchelor vortex and the crossing of oblique shock waves with Mach numbers of 3.5 and 5.0, favourable for supersonic mixing and combustion, respectively. Numerical simulations were conducted to investigate the effects of the circulation intensity and shock angle on vortex breakdown. The results indicate that a breakdown occurs at the shock angle $\beta \geqslant 45^\circ$ or the vortex circulation $q = 0.32$, and the configuration is a bubble structure with a recirculation region; most of the breakdowns possess a stagnation point. Furthermore, the structure differs from that of a normal shock wave and vortex interaction because the bubble region is subsonic and does not comprise a normal shock wave on the inside. Additionally, this vortex breakdown shows that the momentum flux on the centreline decreases once at the tip of the bubble owing to a sudden drop in velocity in the subsonic region. In addition, the enstrophy production resulting from vortex stretching and tilting is found to have a significant advantage in the interaction region. Based on these results, the threshold required for a bubble vortex breakdown was theoretically derived as an inequality. The numerical simulation results support the theoretical criterion obtained from the proposed inequality. Therefore, a streamwise vortex breakdown resulting from the interaction between the vortex and intersecting oblique-shocks should be reasonably predicted.

The present work aims at clarifying the effects of a solid boundary on the salt fingers in the wall-bounded double diffusive convection turbulence driven by the salinity and temperature differences between the top and bottom plates. The fluid properties are the same as the seawater, and two-dimensional direct numerical simulations are conducted over a wide range of the thermal and salinity Rayleigh numbers which measure the strength of driving salinity difference and stabilising temperature difference. We find that the bulk density ratio $\varLambda _b$, defined by the mean temperature and salinity gradients at the bulk, controls the flow morphology. As $\varLambda _b$ exceeds unity, the bulk flow shifts from wide convection rolls to slender salt fingers. Two different regimes are further identified for the cases of salt-finger type. One is the confined salt-finger regime where the characteristic height of salt fingers is comparable to the bulk height and the influences of the solid boundary are noticeable. The other is the free salt-finger regime where the salt fingers are much shorter than the bulk height. In this latter regime, the transport properties versus $\varLambda _b$ are in quantitative agreement with those obtained in the fully periodic domain (e.g. Traxler et al., J. Fluid Mech., vol. 677, 2011, pp. 530–553). For a limited range of density ratio at the highest salinity Rayleigh number considered here, multiple states can be obtained from different initial conditions. The large-scale secondary instability and spontaneous formation of staircase from finger layers are not observed in the current study.

Sound wave propagation in rarefied flows of molecular gases confined in micro-channels is investigated numerically. We first validate the employed kinetic model against the experimental results and then systematically study the gas damping and surface force on the transducer as well as the resonance/anti-resonance in confined space. To quantify the impact of the finite relaxation rates of the translational and internal energies on wave propagation, we examine the roles of bulk viscosity and thermal conductivity in depth over a wide range of rarefactions and oscillation frequencies. It is found that the bulk viscosity only exerts influence on the pressure amplitude and its resonance frequency in the slip regime in high oscillations. In addition, the internal degree of freedom is frozen when the bulk viscosity of a molecular gas is large, resulting in the pressure amplitude of sound waves in the molecular gas being the same as in a monatomic gas. Meanwhile, the thermal conductivity has a limited influence on the pressure amplitude in all the simulated flows. In the case of the thermoacoustic wave, we prove that the Onsager–Casimir reciprocal relation also holds for molecular gases, i.e. the pressure deviation induced by the temperature variation is equal to the heat flux induced by the plate oscillation. Our findings enable an enhanced understanding of sound wave propagation in molecular gases, which may facilitate the design of nano-/micro-scale devices.

The quasigeostrophic shallow-water system on the mid-latitude $\beta$ plane with weak, small-scale turbulent forcing is explored in the limit of large energy. Forcing is weak in the sense that the energy input rate relative to the energy of the flow is very small, of the order of $10^{-5}$–$10^{-10}$, and the potential vorticity assumes an approximate staircase structure. The flow has large energy in the sense that the jet spacing is equal to the domain width so that no further jet mergers can occur. Quasi-stationary numerical experiments, in which the energy grows linearly, reveal late-time quasi-steady, translating solutions comprising a single jet and vortex dipole, with details of the jet-vortex configuration depending on the deformation radius. At a smaller deformation radius the jet may traverse the entire domain in the $y$ direction one or more times, giving a jet orientation that is predominantly north–south, rather than the usual east–west orientation characteristic of $\beta$-plane jets at lower energy. In these meandering cases, a mode number is proposed that quantifies the degree of meandering relative to the vortices. Besides the steadily translating solutions, topological changes in the jet-vortex structure are identified that occur via a transient interaction of a meandering jet with a vortex. At high energy, these give rise to apparently periodic solutions of the system; at low energy, before a single, domain-wide jet is established, they indicate that jet merger may occur through more complicated processes than the simple merging of neighbouring jets.

This work presents an experimental investigation focused on the analysis of aerodynamic properties between two interacting spheres in a supersonic rarefied flow. Atmospheric re-entries of space debris, whether natural or man-made, begin at altitude 120 km, and observations of historical re-entries have shown that fragmentation occurs between 90 and 50 km. The resulting fragments interact with each other, altering their own trajectories while traversing the different flow regimes between the free molecular and continuum regimes. This study focuses on the intermediate slip regime, where viscous effects of varying magnitude can influence the nature of the interactions of the shocks and modify them from the already known behaviour in the continuum regime. Specifically, this study examines how two spheres interact with each other upon re-entry into the atmosphere, focusing particularly on the six types of shock/shock interactions identified by Edney. The experiments were performed in the MARHy wind tunnel, in a steady Mach 4 laminar flow with static pressure 2.67 Pa. To highlight the differences between the six types of interferences, a variety of set-ups and devices were used: flow-field visualization, aerodynamic forces (through two diagnoses, aerodynamic balance and the swinging sphere technique) and wall pressure measurements. Results demonstrate the identification of differences according to the type of interference observed, showing in particular the viscous effect of rarefied flows by making a comparison with the continuum regime.

We demonstrate how to accelerate the computationally taxing process of deep reinforcement learning (DRL) in numerical simulations for active control of bluff body flows at high Reynolds number ($Re$) using transfer learning. We consider the canonical flow past a circular cylinder whose wake is controlled by two small rotating cylinders. We first pre-train the DRL agent using data from inexpensive simulations at low $Re$, and subsequently we train the agent with small data from the simulation at high $Re$ (up to $Re=1.4\times 10^5$). We apply transfer learning (TL) to three different tasks, the results of which show that TL can greatly reduce the training episodes, while the control method selected by TL is more stable compared with training DRL from scratch. We analyse for the first time the wake flow at $Re=1.4\times 10^5$ in detail and discover that the hydrodynamic forces on the two rotating control cylinders are not symmetric.

Linear models, based on stochastically forced linearized equations, are deployed for spectral linear stochastic estimation (SLSE) of the velocity and temperature fluctuations in compressible turbulent channel flows with a bulk Mach number of 1.5. Through comparison with the direct numerical simulation (DNS) data, an eddy-viscosity-enhanced model (eLNS) outperforms the one not enhanced (LNS) in computing the coherence and amplitude ratio of streamwise velocity at different wall-normal heights, but they both largely deviate from DNS regarding the temperature prediction. For further investigation, the eigenspectra and pseudospectra of the linear operators are scrutinized. The eddy viscosity is shown to stabilize the eigenmodes and decrease the non-normality of the vortical modes. Consequently, the relative importance of acoustic and entropy modes increases, and they can contribute 20 % to 55 % of the response growth, which is not supported by DNS. Hence, it is an intrinsic defect of the eLNS model introduced by turbulence modelling. After a procedure of cospectrum decomposition, the contributions of acoustic and entropy components are filtered out. The resulting SLSE quantities for velocity, temperature and their coupling are basically agreeable with DNS, demonstrating that the coherent temperature fluctuation is dominated by advection and other vortical motions, instead of the compressibility effects. Moreover, a parameter study of Reynolds and Mach numbers (from 0.3 to 4) is conducted. The semi-local units are shown to well collapse the velocity SLSE quantities to the incompressible case for streamwise-elongated structures of high coherence.

The flow inside a rotating annulus tilted with respect to gravity is characterized experimentally and theoretically. As in the case of a tilted rotating cylinder the flow is forced by the free surface, maintained flat by gravity. It leads to resonances of global inertial modes (Kelvin modes) when the height of fluid is a multiple of half the wavelength of the mode. The divergence of the mode is saturated by viscous effects at the resonance. The maximum amplitude scales as the Ekman number to the power $-1/2$ when surface Ekman pumping is dominant, and to the power $-1$ when volumic damping is dominant. An analytical prediction is given with no fitting parameter, in excellent agreement with experimental results. At lower Ekman numbers, the flow destabilizes with respect to a triadic resonance instability, as already observed by Xu & Harlander (Phys. Rev. Fluids, 2020). We provide here a linear stability analysis leading to the viscous threshold of the instability for small tilt angles. For large tilt angles, a centrifugal instability is observed due to the acceleration of the flow by the inner cylinder. Finally, the features of the turbulent flow and its mixing efficiency are characterized experimentally. We underline the potential interest of this configuration for bioreactors.