At low Reynolds numbers, the flow through a pipe with a sudden expansion is characterized by the localized occurrence of flow instabilities, with the formation of a so-called turbulence puff. In the literature, physical experiments typically predict earlier occurrence of turbulence than computational fluid dynamics simulations. However, the behaviour of ‘natural’ transition to turbulence without perturbations, and the dependence of transition to turbulence on perturbations, are not yet fully understood, particularly for the simulations. The purpose of the present study is therefore to investigate this flow, including possible sources of perturbation in numerical simulations, and to evaluate their effect on transition to turbulence. Through the exploration of different flow rates, numerical settings and inlet perturbation amplitudes, and by evaluating coarse and refined simulations, insights into low-Reynolds-number transitional turbulent flows are obtained. The turbulence kinetic energy budget of the turbulence puff or slug characteristic of this flow is also evaluated. In conclusion, even when perturbations are not intentionally added, there can still be significant sources of numerical perturbation and error that trigger turbulence in simulations, but perturbations will need to be added in refined simulations in order to produce turbulence. Finally, the results agree with the notion that there may not be a scenario where the flow transitions naturally to turbulence without any perturbation.

In this paper, we consider the steady-state base flow for natural convection in a vertical porous slab with permeable boundaries. Although recent work proposed a one-dimensional solution for this flow, we make a strong case for this flow to be two-dimensional; this centres on an oversight in the use of the Oberbeck–Boussinesq approximation in the earlier work. Two-dimensional numerical solutions for this flow are then obtained using a pressure–temperature formulation, and the results are backed up using asymptotic analysis. The relevance of these findings to other recent work on the stability of convection in porous slabs with permeable boundaries is also briefly discussed.

Acoustic microstreaming is a nonlinear response of a fluid that undergoes high-amplitude acoustic stimulation and tends to viscously absorb it. The present experimental study investigates the generation of acoustic microstreaming induced by an oscillating wall-attached bubble undergoing nonspherical shape modes. From a microscope top view, the formation of particular flow signatures is explored for the main classes of spherical harmonics $Y_{nm}(\theta, \phi )$: zonal ($m = 0 < n$), sectoral ($n = m > 0$) and tesseral ($0 < m < n$) oscillation. The microstreaming induced by a bubble animated by a sectoral mode alone reveals a pattern characterized by a $4n$-lobe flower shape. Tesseral modes give rise to 4m-lobe flower-shaped patterns. Finally, when sectoral and zonal modes coexist, two kinds of pattern stand out: $2n$-lobe flower shape and $n$-pointed star shape. The preferential emergence of one or another streaming pattern is discussed on the basis of the amplitude and phase shift between both shape modes.

Experiments are conducted in a wave tank to investigate wave scattering by a three-dimensional submerged horizontal rectangular plate in a channel. The free-surface elevation around the plate is presented for various water depths and depths of submergence of the plate. The wave forces and moments are obtained using an underwater load measuring system. The numerical simulations are performed with a parallelized three-dimensional boundary element method. The numerical set-up follows closely the set-up of the laboratory experiments. The numerical results are compared with the experimental results for non-breaking waves. In most cases a good agreement is found for the free-surface elevation, the vertical force and the moment. A physical interpretation of the flow around the plate is provided. The pressure distribution on the lower surface of the plate differs from the linear distribution from the leading edge to the trailing edge that is obtained in the equivalent two-dimensional problem. The reflection by the lateral walls is investigated.

A dilute suspension of motile microorganisms subjected to a strong ambient flow, such as algae in the ocean, can be modelled as a population of non-interacting, orientable active Brownian particles (ABPs). Using the Smoluchowski equation (i.e. Fokker–Planck equation in space and orientation), one can describe the non-trivial transport phenomena of ABPs such as taxis and shear-induced migration. This work transforms the Smoluchowski equation into a transport equation, in which the drifts and dispersions can be further approximated as a function of the local flow field. The new model can be applied to any global flow field due to its local nature, unlike previous methods such as those utilising the generalised Taylor dispersion theory. The transformation shows that the overall drift includes both the biased motility of individual particles in the presence of taxis and the shear-induced migration in the absence of taxis. In addition, it uncovers other new drifts and dispersions caused by the interactions between the orientational dynamics and the passive advection–diffusion of ABPs. Finally, the performance of this model is assessed using examples of gyrotactic suspensions, where the proposed model is demonstrated to be most accurate when the biased motility of particles (i.e. taxis) is weak.

This paper presents an experimental study of the interaction of turbulent spots with an initially laminar separation, using schlieren visualisation and dynamic measurements of surface heat transfer and pressure. The separation is generated on a blunt cylinder-flare body, tested at Mach 9, and entropy layer effects result in a boundary layer edge Mach number of 3.43 at separation. A single roughness element is used to produce isolated spots, defined such that separation collapse and re-establishment is completed before arrival of the next spot. On average the spot axial length, at the start of the interaction, is 2.5 times the separation length, growing to 6.8 times as the spot base passes the original reattachment position. As such the spot comprises a large perturbation. The local separation responds almost immediately with passage of the spot, so that the downstream region may be unaffected while the upstream part has already collapsed. Re-establishment of separation is slow, taking up to four times the total transit time of the spot. A basic model is presented to explore the transient wave processes during spot passage.

From geotechnical applications to space exploration, auger drilling is often used as a standard tool for soil sample collection, instrument installation and others. Focusing on granular flow associated with the rotary drilling process, we investigate the performance of auger drilling in terms of sampling efficiency, defined as the mass ratio of the soil sample collected in the coring tube to its total volume at a given penetration depth, by means of experiments, numerical simulations as well as theoretical analysis. The ratio of rotation to penetration speed is found to play a crucial role in the sampling process. A continuum model for the coupled granular flow in both coring and discharging channels is proposed to elucidate the physical mechanism behind the sampling process. Supported by a comparison with experimental results, the continuum model provides a practical way to predict the performance of auger drilling. Further analysis reveals that the drilling process approaches a steady state with constant granular flow speeds in both channels. In the steady state, sampling efficiency decreases linearly with the growth of the rotation to penetration speed ratio, which can be well captured by the analytical solution of the model. The analytical solution also suggests that the sampling efficiency is independent of gravity in the steady state, which has profound implications for extraterrestrial sample collection in future space missions.

This paper presents a model for bubble dynamics in a protein solution, including varying surface tension and dynamic adsorption/desorption of protein onto the bubble surface. We model the protein-coated bubble surface as a linear viscoelastic interface. Two cases are studied to understand the importance of the surface excess stress: (1) bubble dissolution in a protein solution due to gas diffusion; and (2) bubble response to an imposed fluctuating pressure field. In the first case study, the surface excess stress stabilizes the bubble against dissolution. Initially, the surface excess stress is negligible, and the dissolution rate is governed by the Weber number, which compares the gas inertial force and the surface tension force. As the bubble shrinks, the surface excess stress grows and eventually balances the surface tension. After that, the dissolution rate is governed by the protein desorption rate and the elasto-capillary number, which compares the surface tension and the surface dilatational elasticity. Our model predictions for the dissolution process agree with experiments before the bubble buckles. In the second case study, the surface dilatational viscosity and dilatational elasticity add resistance and stiffness to the system, respectively. Including the surface excess stress increases (or reduces) the amplitude of the bubble radius if the frequency of the imposed fluctuating pressure is greater (or less) than a critical value. These results highlight the importance of the surface rheology on the protein-coated bubble dynamics, which has applications in drug delivery and ultrasound contrast agents.

It is recently found that viscoelastic pipe flows can be linearly unstable, leading to the possibility of a supercritical transition route, in contrast to Newtonian pipe flows. Such an instability is referred to as the centre mode, which was studied numerically by Chaudhary et al. (J. Fluid Mech., vol. 908, 2021, p. A11) based on an Oldroyd-B model. In this paper, we are interested in expanding the parameter space investigated and exploring the asymptotic scalings related to this centre instability in the Oldroyd-B viscoelastic pipe flow. It is found from the asymptotic analysis that the centre mode exhibits a three-layered asymptotic structure in the radial direction, a wall layer, a main layer and a central layer, which are driven by pure viscosity, axial and/or radial pressure gradient, and a combined effect of viscosity and elasticity, respectively. Depending on the relations of the control parameters, two regimes, the long-wavelength and short-wavelength centre instabilities, emerge, for which the central-layer thicknesses are of different orders of magnitude. Our large-Reynolds-number asymptotic predictions are compared to the numerical solutions of the original eigenvalue system, and favourable agreement is achieved, especially when the parameters approach their individual limits. In addition to revealing the dominant factors and their balances, the asymptotic analysis describes the instability system by reducing the number of control parameters, and furthermore explaining the collapse of the numerical results for different re-scalings.

Upon drop impact on a surface of comparable size to that of the drop, a sheet is produced that evolves freely in the air, bounded by a rim from which ligaments and droplets are continuously shed. This process is a canonical example of unsteady sheet fragmentation. The sheet dynamics is coupled with continuous ligament and drop shedding (Wang & Bourouiba, J. Fluid Mech., vol. 848, 2018b, 946–967; Wang & Bourouiba, J. Fluid Mech., vol. 910, 2021b, A39) and is governed by a nonlinear non-Galilean Taylor–Culick law (Wang & Bourouiba, 2022 (in press)). Here, we report the results of a combined theoretical and experimental study of the partition and temporal evolution of mass, momentum and energy in each part of the system composed of sheet, rim, ligaments and drops. We elucidate and derive analytical predictions, without fitting parameters, of the temporal evolution of the fractions of volume/mass, momentum and energy in each sub-part of the system: from sheet, to rim to fluid shed. We show that their temporal evolution and partitioning are independent of impact conditions. Interestingly this implies, for example, that the fraction of initial drop volume shed from an impacting drop is independent of the initial energy (or Weber number) of impact. We validate our predictions against precise measurements. Finally, we show that the partition laws for this unsteady fragmentation system are robust to changes of fluid properties (viscosity, surface tension and density). We provide the ranges of validity of our partition law on a Weber–Reynolds numbers regime map.

Free-stream turbulence (FST) induced boundary layer transition is an intricate physical process that starts already at the leading edge (LE) with the LE receptivity process dictating how the broad spectrum of FST scales is received by the boundary layer. The importance of the FST integral length scale, apart from the turbulence intensity, has recently been recognized in transition prediction but a systematic variational study of the LE pressure gradient has still not been undertaken. Here, the LE pressure gradient is systematically varied in order to quantify its effect on the transition location. To this purpose, we present a measurement technique for accurate determination of flat-plate boundary layer transition location. The technique is based on electret condenser microphones which are distributed in the streamwise direction with high spatial resolution. All time signals are acquired simultaneously and post-processed giving the full intermittency distribution of the flow over the plate in a few minutes. The technique is validated against a similar procedure using hot-wire anemometry measurements. Our data clearly shows that the LE pressure gradient plays a decisive role in the receptivity process for small integral length scales, at moderate turbulence intensities, leading to variations in the transitional Reynolds number close to 40 %. To our knowledge, this high sensitivity of LE pressure gradient to transition has so far not been reported and our experiments were therefore partly repeated using another LE to ensure set-up independence and result repeatability.

A direct numerical simulation is performed for a supersonic turbulent boundary layer interacting with a compression/expansion ramp at an angle $\alpha =24^{\circ }$, matching the same operating conditions of the direct numerical simulation by Priebe & Martín (J. Fluid Mech., vol. 699, 2012, pp. 1–49). The adopted numerical method relies on the high-order spectral difference scheme coupled with a bulk-based, low-dissipative, artificial viscosity for shock-capturing purposes (Tonicello et al., Comput. Fluids, vol. 197, 2020, 104357). Filtered and averaged fields are evaluated to study total kinetic energy transfers in the presence of non-negligible compressibility effects. The compression motions are shown to promote forward transfer of kinetic energy down the energy cascade, whereas expansion regions are more likely to experience backscatter of kinetic energy. A standard decomposition of the subgrid scale tensor in deviatoric and spherical parts is proposed to study the compressible and incompressible contributions in the total kinetic energy transfers across scales. On average, the correlation between subgrid scale dissipation and large-scale dilatation is shown to be caused entirely by the spherical part of the Reynolds stresses (i.e. the turbulent kinetic energy). On the other hand, subtracting the spherical contribution, a mild correlation is still noticeable in the filtered fields. For compressible flows, it seems reasonable to assume that the eddy-viscosity approximation can be a suitable model for the deviatoric part of the subgrid scale tensor, which is exclusively causing forward kinetic energy cascade on average. Instead, more complex models are likely to be needed for the spherical part, which, even in statistical average, provides an important mechanism for backscatter.

We present theoretical and numerical results that demonstrate the sensitivity of the shape of a static meniscus in a rectangular channel to localised geometric perturbations in the form of narrow ridges and grooves imposed on the channel walls. The Young–Laplace equation is solved for a gas/liquid interface with fixed contact angle using computations, analytical arguments and semi-analytical solutions of a linearised model for small-amplitude perturbations. We find that the local deformation of the meniscus's contact line near a ridge or groove is strongly dependent on the shape of the perturbation. In particular, small-amplitude perturbations that change the channel volume induce a change in the pressure difference across the meniscus, resulting in long-range curvature of its contact line. We derive an explicit expression for this induced pressure difference directly in terms of the boundary data. We show how contact lines can be engineered to assume prescribed patterns using suitable combinations of ridges and grooves.

We propose a mathematical model from physical principles to predict the sound generated in nozzles with dissipation. The focus is on the sound generated from the acceleration of temperature inhomogeneities (also known as entropy waves), which is referred to as indirect noise. First, we model the dissipation caused by flow recirculation and wall friction with a friction factor, which enables us to derive quasi-one-dimensional equations from conservation laws. The model is valid for both compact nozzles and nozzles with a spatial extent. Second, the predictions from the proposed model are compared against the experimental data available in the literature. Third, we compute the nozzle transfer functions for a range of Helmholtz numbers and friction factors. It is found that the friction and the Helmholtz number have a significant effect on the gain/phase of the reflected and transmitted waves. The analysis is performed from subsonic to supersonic regimes (with and without shock waves). The acoustic transfer functions vary significantly because of non-isentropic effects and the Helmholtz number, in particular, in the subsonic-choked regime. Finally, we calculate the effect that the friction of a nozzle guide vane has on thermoacoustic stability. It is found that the friction and the Helmholtz number can change thermoacoustic stability from a linearly stable regime to a linearly unstable regime. The study opens up new possibilities for the accurate prediction of indirect noise in realistic nozzles with implications on both noise emissions and thermoacoustic stability.

Recent experiments (Guan et al., Phys. Rev. Lett., vol. 116, issue 6, 2016a, p. 066102; Guan et al., Phys. Rev. E, vol. 94, issue 4, 2016b, p. 042802) showed many interesting phenomena on dynamic contact angle hysteresis while there is still a lack of complete theoretical interpretation. In this work, we study the time averaging of the apparent advancing and receding contact angles on surfaces with periodic chemical patterns. We first derive a new Cox-type boundary condition for the apparent dynamic contact angle on homogeneous surfaces using the Onsager variational principle. Based on this condition, we propose a reduced model for some typical moving contact line problems on chemically inhomogeneous surfaces in two dimensions. Multiscale expansion and averaging techniques are employed to approximate the model for asymptotically small chemical patterns. We obtain a quantitative formula for the averaged dynamic contact angles. It describes explicitly how the advancing and receding contact angles depend on the velocity and the chemical inhomogeneity of the substrate. The formula is a coarse-graining version of the Cox-type boundary condition on inhomogeneous surfaces. Numerical simulations are presented to validate the analytical results. The numerical results also show that the formula characterizes well the complicated behaviour of dynamic contact angle hysteresis observed in the experiments.

Opposition flow control is a robust strategy that has been proved effective in turbulent wall-bounded flows. Its conventional set-up consists of measuring wall-normal velocity in the buffer layer and opposing it at the wall. This work explores the possibility of implementing this strategy with a detection plane in the logarithmic layer, where control could be feasible experimentally. We apply control on a channel flow at $Re_\tau = 932$, only on the eddies with relatively large wavelengths ($\lambda / h > 0.1$). Similarly to the buffer layer opposition control, our control strategy results in a virtual-wall effect for the wall-normal velocity, creating a minimum in its intensity. However, it also induces a large response in the streamwise velocity and Reynolds stresses near the wall, with a substantial drag increase. When the phase of the control lags with respect to the detection plane, spanwise-homogeneous rollers are observed near the channel wall. We show that they are a result of a linear instability. In contrast, when the control leads with respect to the detection plane, this instability is inactive and oblique waves are observed. Their wall-normal profiles can be predicted linearly as a response of the turbulent channel flow to a forcing with the advection velocity of the detection plane. The linearity, governing the flow, opens a possibility to affect large scales of the flow in a controlled manner, when enhanced turbulence intensity or mixing is desired.

The accelerations of tracer and light particles (bubbles) in compressible homogeneous isotropic turbulence are investigated by using data from direct numerical simulations up to turbulent Mach number $M_t =1$. For tracer particles, the flatness factor of acceleration components, $F_a$, increases gradually for $M_t \in [0.3, 1]$. On the contrary, $F_a$ for bubbles develops a maximum around $M_t \sim 0.6$. The probability density function of longitudinal acceleration of tracers is increasingly skewed towards the negative value as $M_t$ increases. By contrast, for light particles, the skewness factor of longitudinal acceleration, $S_a$, first becomes more negative with the increase of $M_t$, and then goes back to $0$ when $M_t$ is larger than $0.6$. Similarly, differences among tracers and bubbles appear also in the zero-crossing time of acceleration correlation. It is argued that all these phenomena are intimately linked to the flow structures in the compression regions close to shocklets.

The impact of inlet turbulence on the structure of turbulent channel flow is investigated using particle image velocimetry. Streamwise–wall-normal plane measurements are performed in a channel, where different turbulence intensities were generated at the inlet with an active grid. Four cases are tested with matched centreline mean velocities, while the centreline turbulence intensities ranged from 3.7 % for the reference case, up to 6.4 %. The friction velocity is found to be approximately constant with varying centreline turbulence intensities, resulting in a matched friction Reynolds number of $Re_\tau \approx 770$ for all cases, which contrasts with similar experiments performed in a zero-pressure-gradient boundary layer. The log region remains intact for all cases. The so-called quiescent core of the turbulent channel flow is also investigated. In addition to increased core discontinuity, the increased fluctuations of the streamwise velocity give rise to new core states, which differ from the conventional ones in their characteristic velocity. They are associated with a bulk of low- or high-momentum fluid passing through the measurement domain, and their occurrence increases with turbulence intensity. Tracking the core boundaries indicates an overall tendency of the core to move closer to the wall for increased inlet turbulence intensities, resulting in an increased core thickness. Moreover, it is found that the low-momentum cores generally reside closer to the wall compared with the ordinary cores and appear to be thicker than them, whereas the opposite, i.e. residing farther from the wall and being thinner, is true for the high-momentum cores.

We consider a dilute gas of electrically charged granular particles in the homogeneous cooling state. We derive the energy dissipation rate and the transport coefficients from the inelastic Boltzmann equation. We find that the deviation of the velocity distribution function from the Maxwellian yields overshoots of the transport coefficients, and especially, the negative peak of the Dufour-like coefficient, $\mu$, in the intermediate granular temperature regime. We perform the linear stability analysis and investigate the granular temperature dependence of each mode, where the instability mode is found to change against the granular temperature. The molecular dynamics simulations are also performed to compare the result with that from the kinetic theory.

Biological membranes are host to proteins and molecules which may form domain-like structures resulting in spatially varying material properties. Vesicles with such heterogeneous membranes can exhibit intricate shapes at equilibrium and rich dynamics when placed into a flow. Under the assumption of small deformations and a two-dimensional system, we develop a reduced-order model to describe the fluid-structure interaction between a viscous background shear flow and an inextensible membrane with spatially varying bending stiffness and spontaneous curvature. Material property variations of a critical magnitude, relative to the flow rate and internal/external viscosity contrast, can set off a qualitative change in the vesicle dynamics. A membrane of nearly constant bending stiffness or spontaneous curvature undergoes a small amplitude swinging motion (which includes tangential tank-treading), while for large enough material variations the dynamics pass through a regime featuring tumbling and periodic phase-lagging of the membrane material, and ultimately for very large material variation to a rigid-body tumbling behaviour. Distinct differences are found for even and odd spatial modes of domain distribution. Full numerical simulations are used to probe the theoretical predictions, which appear valid even when studying substantially deformed membranes.