Near-critical fluids subject to simultaneous thermal quench and an imposed external acceleration field are reported to develop ‘sink zones’, where the temperature in the bulk falls below the imposed boundary value. This anomalous cooling effect persists for a long period of time corresponding to the diffusive elimination of the cold boundary layer. The sink-zone phenomenon has been captured previously in numerical simulations (Zappoli et al., J. Fluid Mech, vol. 316, 1996, pp. 53–72; Sharma et al., Phys. Rev E, vol. 96, 2017, 063102; Sharma et al., Phys. Fluids, vol. 29, 2017, 126103) and was observed experimentally (Beysens et al., Phys. Rev. E, vol. 84, 2011, 051201). The present work provides a detailed and thorough theoretical analysis and interpretation based on matched asymptotic expansions. By examining the one-dimensional transient flow and temperature with a mean-field approach, we provide further insight into this striking phenomenon, showing that the behaviour involved is unique to highly compressible near-critical van der Waals gases. We also show that the sub-cooling phenomenon cannot be predicted in perfect gases unless very extreme conditions are applied.

We study a two-dimensional (2-D) potential flow of an ideal fluid with a free surface with decaying conditions at infinity. By using the conformal variables approach, we study a particular solution of the Euler equations having a pair of square-root branch points in the conformal plane, and find that the analytic continuation of the fluid complex potential and conformal map define a flow in the entire complex plane, excluding a vertical cut between the branch points. The expanded domain is called the ‘virtual’ fluid, and it contains a vortex sheet whose dynamics is equivalent to the equations of motion posed at the free surface. The equations of fluid motion are analytically continued to both sides of the vertical branch cut (the vortex sheet), and additional time invariants associated with the topology of the conformal plane and Kelvin's theorem for a virtual fluid are explored. We called them ‘winding’ and virtual circulation. This result can be generalized to a system of many cuts connecting many branch points, resulting in a pair of invariants for each pair of branch points. We develop an asymptotic theory that shows how a solution originating from a single vertical cut forms a singularity at the free surface in infinite time, the rate of singularity approach is double exponential and supersedes the previous result of the short branch cut theory with finite time singularity formation. The present work offers a new look at fluid dynamics with a free surface by unifying the problem of motion of vortex sheets, and the problem of 2-D water waves. A particularly interesting question that arises in this context is whether instabilities of the virtual vortex sheet are related to breaking of steep ocean waves when gravity effects are included.

We examine the vapour cloud of a pure liquid evaporating from a millimetric cylindrical well/cavity/aperture. This is accomplished by injecting the liquid up a vertical pipe towards its outlet onto a horizontal substrate. The injection is halted before the liquid surpasses the substrate level. The resulting final state is a meniscus at or near the pipe's end. The analysis is realised by vapour interferometry (side view over the substrate) closely intertwined with simulations (including Stefan flow), which also help to fill up certain gaps in the measurements and provide computed evaporation rates. Comparison with experiment is facilitated by converting the computed vapour clouds into interferometric images, especially helpful when an inverse (Abel-type) conversion is difficult. Experiments are conducted in both microgravity (via parabolic flights) and ground conditions, thus enabling direct assessment of the role of gravity. The contrast is accentuated by a working liquid with heavy vapour (refrigerant HFE-7100), when instead of being flattened on ground the vapour cloud assumes a roughly hemispherical shape in microgravity. Furthermore, a non-trivial vapour-cloud response to the flight ${\rm g}$-jitter (residual gravity oscillations) is unveiled, ${\rm g}$-jitter vibrations posing a challenge for interferometry itself. A number of undesired but curious side issues are revealed. One concerns vapour formed deep inside the pipe during rapid injection and subsequently ejected into the field of view, which is detected experimentally and quantified in terms of vapour Taylor dispersion in the pipe. Others are an injection volume anomaly and parasitic postinjection specifically observed in microgravity conditions.

Small heavy particles cannot be attracted into a region of closed streamlines in a non-accelerating frame (Sapsis & Haller, Chaos, vol. 20, issue 1, 2010, 017515). In a rotating system of vortices, however, particles can get trapped (Angilella, Physica D, vol. 239, issue 18, 2010, pp. 1789–1797) in the vicinity of vortices. We perform numerical simulations to examine trapping of inertial particles in a prototypical rotating flow described by a rotating pair of Lamb–Oseen vortices of identical strength, in the absence of gravity. Our parameter space includes the particle Stokes number $St$, which is a measure of the particle's inertia, and a density parameter $R$, which measures the particle's density relative to the fluid. In particular, we study the regime $0< R<1$ and $0< St<1$, which corresponds to an inertial particle that is finitely denser than the fluid. We show that in this regime, a significant fraction of particles can be trapped indefinitely close to the vortices, and display extreme clustering into objects of smaller dimension: attracting fixed points and limit cycles of different periods including chaotic attractors. As $St$ increases for a given $R$, we may have an incomplete or complete period-doubling route to chaos, as well as an unusual period-halving route back to a fixed point attractor. The fraction of trapped particles can be a non-monotonic function of $St$, and we may even have windows in $St$ for which no particle trapping occurs. At $St$ larger than a critical value, beyond which trapping ceases to exist, significant fractions of particles can spend long but finite times in the vortex vicinity. The inclusion of the Basset–Boussinesq history (BBH) force is imperative in our study due to the finite density of the particle. We observe that the BBH force significantly increases the basin of attraction over which trapping occurs, and also widens the range of $St$ for which trapping can be realised. Extreme clustering can be of significance in a host of physical applications, including planetesimal formation by aggregation of dust in protoplanetary discs, and aggregation of phytoplankton in the ocean. Our findings in the prototypical model provide impetus to conduct experiments and further numerical investigations to understand clustering of inertial particles.

We report a numerical investigation of a previously noticed but less explored flow state transition in two-dimensional turbulent Rayleigh–Bénard convection. The simulations are performed in a square domain over a Rayleigh number range of $10^7 \leq Ra \leq 2 \times 10^{11}$ and a Prandtl number range of $0.25 \leq Pr \leq 20$. The transition is characterized by the emergence of multiple satellite eddies with increasing $Ra$, which orbit around and interact with the main vortex roll in the system. Consequently, the main roll is squeezed to a smaller size compared with the domain and wanders around in the bulk region irregularly and extensively. This is in sharp contrast to the flow state before the transition, which is featured by a domain-sized circulatory roll with its vortex centre ‘condensed’ near the domain's centre. Detailed velocity field analysis reveals that there exists an abrupt increase in the energy fluctuations of the Fourier modes during the transition. Based on this phase-transition-like signal, the critical condition for the transition is found to follow a scaling relation as $Ra_t \sim Pr^{1.41}$ where $Ra_t$ is the critical Rayleigh number for the transition. This scaling relation is quantitatively explained by a phenomenological model grounded on the bistability behaviour (i.e. spontaneous and stochastic switching between the two flow states) observed at the edge of the transition. The model can also account for the effects of aspect ratio on the transition reported in the literature (van der Poel et al., Phys. Fluids, vol. 24, 2012).

We consider the stability of laminar high-Reynolds-number flow through a planar channel formed by a rigid wall and a heavy compliant wall under longitudinal tension with motion resisted by structural damping. Numerical simulations indicate that the baseline state (with Poiseuille flow and a flat wall) exhibits two unstable normal modes: the Tollmien–Schlichting (TS) mode and a surface-based mode which manifests as one of two flow-induced surface instabilities (FISI), known as travelling wave flutter (TWF) and static divergence (SD), respectively. In the absence of wall damping the system is unstable to TWF, where the neutrally stable wavelength becomes shorter as the wall mass increases. With wall damping, TWF is restricted to long wavelengths through interaction with the most unstable centre mode, while for wall damping greater than a critical value the system exhibits an SD mode with a two branch neutral stability curve; the critical conditions along the upper and lower branches are constructed in the limit of large wall damping. We compute the Reynolds–Orr and activation energy descriptions of these neutrally stable FISI by continuing the linear stability analysis to the following order in perturbation amplitude. We find that both FISI are primarily driven by the working of normal stress on the flexible wall, lower-branch SD has negative activation energy, while upper-branch SD approaches zero activation energy in the limit of large wall damping. Finally, we elucidate interaction between TS and TWF modes for large wall mass, resulting in stable islands within unstable regions of parameter space.

We investigate the coupling effects of the two-phase interface, viscosity ratio and density ratio of the dispersed phase to the continuous phase on the flow statistics in two-phase Taylor–Couette turbulence at a system Reynolds number of $6\times 10^3$ and a system Weber number of 10 using interface-resolved three-dimensional direct numerical simulations with the volume-of-fluid method. Our study focuses on four different scenarios: neutral droplets, low-viscosity droplets, light droplets and low-viscosity light droplets. We find that neutral droplets and low-viscosity droplets primarily contribute to drag enhancement through the two-phase interface, whereas light droplets reduce the system's drag by explicitly reducing Reynolds stress due to the density dependence of Reynolds stress. In addition, low-viscosity light droplets contribute to greater drag reduction by further reducing momentum transport near the inner cylinder and implicitly reducing Reynolds stress. While interfacial tension enhances turbulent kinetic energy (TKE) transport, drag enhancement is not strongly correlated with TKE transport for both neutral droplets and low-viscosity droplets. Light droplets primarily reduce the production term by diminishing Reynolds stress, whereas the density contrast between the phases boosts TKE transport near the inner wall. Therefore, the reduction in the dissipation rate is predominantly attributed to decreased turbulence production, causing drag reduction. For low-viscosity light droplets, the production term diminishes further, primarily due to their greater reduction in Reynolds stress, while reduced viscosity weakens the density difference's contribution to TKE transport near the inner cylinder, resulting in a more pronounced reduction in the dissipation rate and consequently stronger drag reduction. Our findings provide new insights into the physics of turbulence modulation by the dispersed phase in two-phase turbulence systems.

The geometrical properties of streamlines, such as the curvatures, directions and positions, are studied in steady inviscid compressible flow fields via differential geometry theories and conservation laws. The influences of the streamline geometries on the flow speeds and pressures are also identified and discussed. By transforming the streamlines to fill the domain and satisfy the boundary conditions, a unified geometry-based solver, the streamline transformation method, is proposed for both subsonic and supersonic regions. The governing equations and boundary conditions along streamlines and shock waves are also derived. This method is verified by numerical results of three typical flow fields, including the subsonic channel flow, the supersonic downstream of attached shock waves and especially the subsonic/supersonic downstream of detached bow shock waves. Both two-dimensional planar and axisymmetric flow fields are considered. Compared with the results from computational fluid dynamics, good agreements are achieved by this method, while fewer computational resources, by an order of magnitude, are consumed. Features of these flow fields are also analysed from a geometrical perspective, such as flow speeds and pressures deviated by the wall curvatures, and three-dimensional effects in the after-shock flow fields. For a hyperbolic-shaped bow shock wave, the stand-off distances and the transitions from subsonic to supersonic regions are also discussed. As indicated by the accuracy, efficiency and applicability in a wide range of flow speeds, the streamline transformation method would be a potential candidate for the theoretical analysis and inverse design of high-speed flow fields, especially where the subsonic regions exist downstream of strong shock waves.

Over the last decade, substantial progress has been made in understanding the topology of quasi-two-dimensional (2-D) non-equilibrium fluid flows driven by ATP-powered microtubules and microorganisms. By contrast, the topology of three-dimensional (3-D) active fluid flows still poses interesting open questions. Here, we study the topology of a spherically confined active flow using 3-D direct numerical simulations of generalized Navier–Stokes (GNS) equations at the scale of typical microfluidic experiments. Consistent with earlier results for unbounded periodic domains, our simulations confirm the formation of Beltrami-like bulk flows with spontaneously broken chiral symmetry in this model. Furthermore, by leveraging fast methods to compute linking numbers, we explicitly connect this chiral symmetry breaking to the entanglement statistics of vortex lines. We observe that the mean of linking number distribution converges to the global helicity, consistent with the asymptotic result by Arnold [In Vladimir I. Arnold – Collected Works (ed. A.B. Givental, B.A. Khesin, A.N. Varchenko, V.A. Vassiliev & O.Y. Viro), pp. 357–375. Springer]. Additionally, we characterize the rate of convergence of this measure with respect to the number and length of observed vortex lines, and examine higher moments of the distribution. We find that the full distribution is well described by a k-Gamma distribution, in agreement with an entropic argument. Beyond active suspensions, the tools for the topological characterization of 3-D vector fields developed here are applicable to any solenoidal field whose curl is tangent to or cancels at the boundaries of a simply connected domain.

Motivated by the recent numerical results of Khalid et al. (Phys. Rev. Lett., vol. 127, 2021, 134502), we consider the large-Weissenberg-number ($W$) asymptotics of the centre mode instability in inertialess viscoelastic channel flow. The instability is of the critical layer type in the distinguished ultra-dilute limit where $W(1-\beta )=O(1)$ as $W \rightarrow \infty$ ($\beta$ is the ratio of solvent-to-total viscosity). In contrast to centre modes in the Orr–Sommerfeld equation, $1-c=O(1)$ as $W \rightarrow \infty$, where $c$ is the phase speed normalised by the centreline speed as a central ‘outer’ region is always needed to adjust the non-zero cross-stream velocity at the critical layer down to zero at the centreline. The critical layer acts as a pair of intense ‘bellows’ which blows the flow streamlines apart locally and then sucks them back together again. This compression/rarefaction amplifies the streamwise-normal polymer stress which in turn drives the streamwise flow through local polymer stresses at the critical layer. The streamwise flow energises the cross-stream flow via continuity which in turn intensifies the critical layer to close the cycle. We also treat the large-Reynolds-number ($Re$) asymptotic structure of the upper (where $1-c=O(Re^{-2/3})$) and lower branches of the $Re$–$W$ neutral curve, confirming the inferred scalings from previous numerical computations. Finally, we remark that the viscoelastic centre-mode instability was actually first observed in viscoelastic Kolmogorov flow by Boffetta et al. (J. Fluid Mech., vol. 523, 2005, pp. 161–170).

Water particle orbits are key elements in the Lagrange wave formulation. The stochastic Miche implementation of the Lagrange model is a linear Gaussian two-dimensional or three-dimensional space–time model which exhibits typical nonlinear wave characteristics when transformed to Eulerian coordinates. This paper investigates the statistical relation between the degree of front–back asymmetry of individual waves and the orbit orientation for the particle located at the wave maximum at the point of observation. It is shown that, in the Lagrangian model with statistical front–back symmetry, for individual waves there is a clear connexion between the degree of individual wave asymmetry and the orientation of the randomly deformed elliptic orbit: a steep front correlates with upward tilt, a steep back is correlated with a downward tilt. This holds both for waves observed in time and in space, and the dependence is stronger for large amplitude waves than for smaller ones. The dependence is strongly dependent on the depth and on the significant steepness and spectral width. Inclusion of the average Stokes drift has a moderate effect on the dependence. For models with forced front–back asymmetry there is both a systematic dependence and a statistical correlation between asymmetry and tilt; for large amplitude waves the systematic relation dominates. The conclusions are based on Fourier simulations of Gauss–Lagrange waves of first and second order with a wind–sea Pierson–Moskowitz spectrum and a narrow swell JONSWAP spectrum.