Superhydrophobic surfaces dramatically reduce the skin friction of overlying liquid flows, providing a lubricating layer of gas bubbles trapped within their surface nano-sculptures. Under wetting-stable conditions, different models can be used to numerically simulate their effect on the overlying flow, ranging from spatially homogeneous slip conditions at the wall, to spatially heterogeneous slip–no-slip conditions taking into account or not the displacement of the gas–water interfaces. These models provide similar results in both laminar and turbulent regimes, but their effect on transitional flows has not been investigated yet. In this work we study, by means of numerical simulations and global stability analyses, the influence of the modelling of superhydrophobic surfaces on laminar–turbulent transition in a channel flow. For the K-type scenario, a strong transition delay is found using spatially homogeneous or heterogeneous slippery boundaries with flat, rigid liquid–gas interfaces. Whereas, when the interface dynamics is taken into account, the time to transition is reduced, approaching that of a no-slip channel flow. It is found that the interface deformation promotes ejection events creating hairpin heads that are prone to breakdown, reducing the transition delay effect with respect to flat slippery surfaces. Thus, in the case of modal transition, the interface dynamics must be taken into account for accurately estimating transition delay. Contrariwise, non-modal transition triggered by a broadband forcing is unaffected by the presence of these surfaces, no matter the surface modelling. Thus, superhydrophobic surfaces may or not influence transition to turbulence depending on the interface dynamics and on the considered transition process.

In homogeneous isotropic turbulence, slender rods are known to align with the Lagrangian stretching direction. However, how the degree of alignment depends on the aspect ratio of the rod is not understood. Moreover, particle-laden flows are often anisotropic and inhomogeneous. Therefore we study the alignment of rods with the Lagrangian stretching direction in a channel flow, which is approximately homogeneous and isotropic near the centre but inhomogeneous and anisotropic near the walls. Our main question is how the distribution of relative angles between a rod and the Lagrangian stretching direction depends on the aspect ratio of the rod and upon the distance of the rod from the channel wall. We find that this distribution exhibits two regimes: a plateau at small angles corresponding to random uncorrelated motion, and power-law tails due to large excursions. We find that slender rods near the channel centre align better with the Lagrangian stretching direction compared with those near the channel wall. These observations are explained in terms of simple statistical models based on Jeffery's equation, qualitatively near the channel centre and quantitatively near the channel wall. Lastly we discuss the consequences of our results for the distribution of relative angles between the orientations of nearby rods (Zhao et al., Phys. Rev. Fluids, vol. 4, 2019, 054602).

The flow topology and leading-edge vortex (LEV) formation and detachment mechanism of a pitching and plunging flat plate are experimentally investigated in this study. Focus is placed on three novel aspects. First, to examine the differences between start-up and cyclic motions, the flow fields of one-shot experiments are compared to cyclic cases. The results show that the start cycle has very limited effect on the cyclic LEV development and flow topology evolution. Next, the influence of the maximum effective angle of attack on the LEV development in cyclic motion is introduced. Different secondary structures that lead to the detachment of LEV are found with variation of maximum effective angle of attack. Depending on the leading-edge shear-layer angle, three different flow topologies develop on the plate: quasi-steady development, boundary-layer eruption and secondary vortex formation. Which of these three topological scenarios occurs depends entirely on the maximum effective angle of attack. A vortex Reynolds number based on the transition time of the leading-edge shear-layer angle is defined to quantitatively assess which of the flow topologies will appear. Finally, a simplified model to describe the observed LEV growth is proposed, based on the assumptions that the velocity is constant at the outer vortex boundary and that the vortex boundary is a circular arc starting from the leading edge. The LEV circulation growth is found to increase linearly with the combination of the effective inflow velocity and the effective angle of attack.

The flow physics associated with the interaction of a low aspect ratio, cantilevered cylindrical pin with a flow over a flat plate was investigated experimentally using oil visualizations and stereoscopic particle image velocimetry. The interactions of the vortical structures were explored for laminar, transitional and turbulent incoming boundary layers, where the flow's sensitivity to the pin's aspect ratio and its relative submergence within the boundary layer was studied. The surrounding flow is highly sensitive to subtle changes in these parameters (both are order 1) due to strong dependence between the flow over the pin's free end and its wake. These flow structures are heavily influenced by competing mechanisms of self-induction and shear flow due to outer fluid entrainment and the proximity to the wall. In particular, the observed vortical features exhibit strong inter-dependencies in the near wake. For a turbulent boundary layer, the resultant ‘arch-like’ structure is observed to be slightly stretched in the axial direction. Whereas, under laminar inflow conditions, the reduced shear and turbulence intensity facilitate a wider wake and a stronger downwash from the leeward edge, resulting in a concave ‘M-shaped’ vortex, affecting the formation and evolution of the trailing vortex pair. In addition, larger aspect ratios result in an increased magnitude of downwash into the wake, which re-energizes the near-wall flow. Whereas, for lower aspect ratios, the level of interaction between vortical features decreases due to a reduced downwash and weaker shear. These flow characteristics are discussed in detail in the paper.

We experimentally and theoretically investigate the dynamics of a partially wetting water droplet subject to a two-dimensional high-speed jet of air blowing perpendicularly to the substrate. When the jet velocity is above a critical value, the droplet evolves under wind and splits into two secondary drops. In addition to droplet splitting, we observe depinning of the droplet on one side when the jet is applied at a small distance from the initial centre of the droplet. In parallel with systematic experiments, we develop a mathematical model to compute the coupled evolution of the droplet and an idealised stagnation-point flow. Our simplified lubrication model yields a criterion for the critical jet velocity, as well as the time scale of the droplet breakup, in qualitative agreement with the experiments.

This paper deals with homogenization of flow in porous media with large inhomogeneities. Classical homogenization relies on representative elementary volumes (REV) large enough that asymptotic macroscopic parameters, e.g. effective permeabilities, can be employed to describe the expected or mean behaviour. In this way, Darcy's law, which describes the relationship between macroscopic pressure gradient and volumetric flow rate, was derived. In the presence of large features, however, the required REV size may reach the same order as the geometric reference scale of the problem, and thus effective permeabilities obtained from classical homogenization studies may be unsuited. This is in particular the case for reservoirs with isolated, highly conductive fractures. To see this, consider flow from left to right through a block of finite size. If the latter is small enough, such that some fractures are connected to both left and right boundaries, then the resulting flow will be larger for the same average pressure gradient than through a wider block. In this paper, a new sub-REV continuum model to describe this pre-asymptotic flow behaviour is presented. The model relies on a non-local multi-media description based on coupled integral–differential equations. The only empirical information required for calibration is the effective permeability of an infinitely large domain, e.g. as obtained from classical homogenization. With a series of numerical studies and comparison with Monte Carlo reference data it is demonstrated that the devised sub-REV model accurately captures mean flow rates and pressure profiles for arbitrary domain sizes.

This paper describes a theoretical study – in the time domain – of sound from the interaction of the steady component of the viscous wakes of an upstream propeller with a downstream contra-rotating propeller blade. The study incorporates a two-dimensional model of the upstream propeller wakes and a quasi-three-dimensional blade response function that accounts for downstream blade sweep. For a blade with a straight leading edge, the sound at the observer location, radiated from each blade radius, consists of a series of impulses whose peaks are shown to be influenced by micro Doppler effects and to correspond to the impingement of the propeller wake centrelines on the leading edge of the downstream blade. For radiation from the entire blade span, it is shown that constructive interference of the impulses from all radii can produce impulsive sound of very high amplitude, whereas dephasing of these impulses can reduce significantly the total acoustic signal. For a downstream propeller blade with a swept leading edge, it is shown how the sweep can be designed to ensure that these impulses are de-phased, resulting in significantly lower-amplitude sound at selected observer locations. Finally, to guarantee that the radiated sound is reduced at all possible observer locations, it is shown that the blade leading-edge sweep must be large enough that the trace velocity of the wake centreline, across the leading edge of the downstream propeller blade, is subsonic across the entire span. The benefits are demonstrated for representative blade designs.

A numerical model that allows one to study numerically the evolution of waves along the test section of a wind-wave tank is offered. The simulations are directly related to wind-wave tank experiments carried out for a range of steady wind velocities. At each wind forcing condition, the evolving wind-wave field is strongly non-homogeneous, with wave energy growth along the test section accompanied by frequency downshifting. The wave parameters measured at a short fetch serve as a basis for generating numerous realizations of the initial conditions in the Monte Carlo numerical simulations. The computations are based on a modified unidirectional spatial version of the Zakharov equation that accounts for wind input and dissipation and is applicable for the whole range of wind velocities employed. The model contains two empirical parameters that are selected by comparison of the experimental and numerical results; the same values of those parameters are applied for all wind forcing conditions. The availability of an experimentally verified numerical model allows one to study the contributions of nonlinear wave–wave interactions, dissipation and wind input separately. Special attention is given to accounting for the three-dimensional and random nature of wind waves as observed in experiments. The suggested model combines approaches adopted in the wind-wave growth theories by Miles and Phillips.

Although the thermal conductivity of molecular gases can be measured straightforwardly and accurately, it is difficult to experimentally determine its separate contributions from the translational and internal motions of gas molecules. Yet, this information is critical in rarefied gas dynamics as the rarefaction effects corresponding to these motions are different. In this paper, we propose a novel methodology to extract the translational thermal conductivity (or equivalently, the translational Eucken factor) of molecular gases from the Rayleigh–Brillouin scattering (RBS) experimental data. From the numerical simulation of the Wu et al. (J. Fluid Mech., vol. 763, 2015, pp. 24–50) model we find that, in the kinetic regime, in addition to bulk viscosity, the RBS spectrum is sensitive to the translational Eucken factor, even when the total thermal conductivity is fixed. Thus it is not only possible to extract the bulk viscosity, but also the translational Eucken factor of molecular gases from RBS light scattering spectra measurements. Such experiments bear the additional advantage that gas–surface interactions do not affect the measurements. By using the Wu et al. model, bulk viscosities (due to the rotational relaxation of gas molecules only) and translational Eucken factors of $\textrm {N}_2$, $\textrm {CO}_2$ and $\textrm {SF}_6$ are simultaneously extracted from RBS experiments.

Advective–diffusive transport of passive scalars in confined environments (e.g. vessels and channels) within a network is of fundamental importance in a plethora of biological and geophysical phenomena. We conduct a leading-order analysis, consistent with the theory of hydrodynamic dispersion, which averages out the radial variability within a vessel. One-dimensional solutions for individual vessels (edges of a network), obtained for arbitrary (undefined) transient Dirichlet boundary conditions, serve as a building block for a network model. A network transport solution is developed by iteratively linking single-vessel solutions to each other in a bifurcating fractal tree model, i.e. at nodes of the network. We find transport behaviour to be strongly affected by the network geometry and daughter vessels to significantly impact the rate of transport in the upstream parent vessels.

The interplay of particles and viscoelasticity in turbulent channel flow is studied using direct numerical simulations. The particle concentration is moderate at 20 % solid volume fraction, and the range of fluid elasticity spans from zero for Newtonian fluid to high Weissenberg numbers, $Wi = 25$. Qualitative changes in the flow dynamics are observed compared with dilute suspensions which were studied previously and are known to promote the cycles of hibernating and active turbulence. In contrast, at moderate concentration of particles, these cycles are entirely absent at the same level of fluid elasticity. In addition, instead of the commonly anticipated polymer drag reduction, a drag increase is observed when elasticity exceeds a threshold Weissenberg number. The higher drag is examined at various scales, starting from a global stress balance and down to the level of the particle microstructure. A key factor is the increase in polymer stresses, while the Reynolds shear stress is nearly eradicated. An explanation is provided by analysing the polymer conformation tensor using appropriate measures of its departure from the equilibrium state, with particular focus on the fluid in the vicinity of the particles. It is also demonstrated that viscoelasticity markedly affects both the diffusion and migration dynamics of the particles: diffusion is inhibited due to suppression of turbulent activity and, as a result, reduced mixing of particles and faster decorrelation of their motion; migration is preferential towards the channel centre, which leads to appreciable clustering in that region, which has a direct impact on the local polymer stresses.

Based on an accurate numerical solution of the kinetic equation using well-resolved spatial and velocity grids, the separation of rarefied gas flow in a microchannel with double rectangular bends is investigated over a wide range of Knudsen and Reynolds numbers. Rarefaction effects are found to play different roles in flow separation (vortex formation) at the concave and convex corners. Flow separations near the concave and convex corners are only observed for a Knudsen number up to $0.04$ and $0.01$, respectively. With further increase of the Knudsen number, flow separation disappears. Due to the velocity slip at the solid walls, the concave (convex) vortex is suppressed (enhanced), which leads to the late (early) onset of separation of rarefied gas flows with respect to the Reynolds number. The critical Reynolds numbers for the emergence of concave and convex vortices are found to be as low as $0.32\times 10^{-3}$ and $30.8$, respectively. The slip velocity near the concave (convex) corner is found to increase (decrease) when the Knudsen number increases. An adverse pressure gradient appears near the concave corner for all the examined Knudsen numbers, while for the convex corner it only occurs when the Knudsen number is less than $0.1$. Due to the secondary flow and adverse pressure gradient near the rectangular bends, the mass flow rate ratio between the bent and straight channels of the same length is a non-monotonic function of the Knudsen number. Our results clarify the diversified and often contradictory observations reported in the literature about flow rate enhancement and vortex formation in bent microchannels.

We perform large-eddy simulation (LES) and theoretical analysis to investigate the effects of opposing waves on overlying turbulent wind. The LES results show that opposing waves induce nearly antisymmetric vertical velocity $\tilde {w}$ in the wind on the two sides of the wave crest, while the streamwise velocity $\tilde {u}$ away from the surface and the air pressure $\tilde {p}$ seem symmetric. To study the mechanisms for the wave-induced airflow, we develop a viscous model by linearising the phase-averaged Navier–Stokes equations in the mapped computational curvilinear coordinate. To illustrate the flow dynamics, we split $\tilde {w}$ into an antisymmetric component and a symmetric component. The solution of the antisymmetric component of $\tilde {w}$ from the viscous curvilinear model agrees well with the LES results for different opposing wave conditions. According to the viscous curvilinear model, the large-magnitude antisymmetric component of $\tilde {w}$ is driven by the wave kinematics at the surface and amplified by the mean shear and viscous stress in the air, and it causes the strong symmetric components of $\tilde {u}$ and $\tilde {p}$. In contrast, the small-magnitude symmetric component of $\tilde {w}$ is forced by the antisymmetric $\tilde {w}$ through viscous and turbulent stresses near the surface, and it can be described by a further simplified inviscid curvilinear model away from the surface. It is discovered that the weak symmetric $\tilde {w}$ causes a slight asymmetry in $\tilde {u}$ and $\tilde {p}$, and generates a mean wave-coherent stress and the form drag on the wave surface. The wave attenuation rates quantified using the form drag agree with the published experiments.

Many exact coherent states (ECS) arising in wall-bounded shear flows have an asymptotic structure at extreme Reynolds number $Re$ in which the effective Reynolds number governing the streak and roll dynamics is $\mathit {O}(1)$. Consequently, these viscous ECS are not suitable candidates for quasi-coherent structures away from the wall that necessarily are inviscid in the mean. Specifically, viscous ECS cannot account for the singular nature of the inertial domain, where the flow self-organizes into uniform momentum zones (UMZs) separated by internal shear layers and the instantaneous streamwise velocity develops a staircase-like profile. In this investigation, a large-$Re$ asymptotic analysis is performed to explore the potential for a three-dimensional, short streamwise- and spanwise-wavelength instability of the embedded shear layers to sustain a spatially distributed array of much larger-scale, effectively inviscid streamwise roll motions. In contrast to other self-sustaining process theories, the rolls are sufficiently strong to differentially homogenize the background shear flow, thereby providing a mechanistic explanation for the formation and maintenance of UMZs and interlaced shear layers that respects the leading-order balance structure of the mean dynamics.

The collapse of a gas or vapour bubble near a solid boundary produces a jet directed towards the boundary. High surface pressure and shear stress induced by this jet can damage, or clean, the surface. More complex geometries will result in changes in collapse behaviour, in particular the direction of the jet. The majority of prior research has focused on simple flat boundaries or cases with limited complexity. There is currently very little known about how complex geometries affect bubble collapse. We numerically and experimentally investigate how a slot in a flat boundary affects the jet direction for a single bubble. We use a boundary element model to predict how the jet direction depends on key geometric parameters and show that the results collapse to a single curve when the parameters are normalised appropriately. We then experimentally validate the predictions using laser-induced cavitation and compare the experimental results to the predicted dependencies. This research reveals a tendency for the jet to be directed away from a slot and shows that the jet direction is independent of slot height for slots of sufficient height.

We present an experimental study on controlling the number of vortices and the torque in a Taylor–Couette flow of water for Reynolds numbers from 660 to 1320. Different flow states are achieved in the annulus of width $d$ between the inner rotating and outer stationary cylinders through manipulating the initial height of the water annulus. We show that the torque exerted on the inner cylinder of the Taylor–Couette system can be reduced by up to 20 % by controlling the flow at a state where fewer than the nominal number of vortices develop between the cylinders. This flow state is achieved by starting the system with an initial water annulus height $h_0$ (which nominally corresponds to $h_0/d$ vortices), then gradually adding water into the annulus while the inner cylinder keeps rotating. During this filling process the flow topology is so persistent that the number of vortices does not increase; instead, the vortices are greatly stretched in the axial (vertical) direction. We show that this state with stretched vortices is sustainable until the vortices are stretched to around 2.05 times their nominal size. Our experiments reveal that by manipulating the initial height of the liquid annulus we are able to generate different flow states and demonstrate how the different flow states manifest themselves in global momentum transport.

We investigate the spatial organization and temporal dynamics of large-scale, coherent structures in turbulent Rayleigh–Bénard convection via direct numerical simulation of a 6.3 aspect-ratio cylinder with Rayleigh and Prandtl numbers of $9.6\times 10^7$ and $6.7$, respectively. Fourier modal decomposition is performed to investigate the structural organization of the coherent turbulent motions by analysing the length scales, time scales and the underlying dynamical processes that are ultimately responsible for the large-scale structure formation and evolution. We observe a high level of rotational symmetry in the large-scale structure in this study and that the structure is well described by the first four azimuthal Fourier modes. Two different large-scale organizations are observed during the duration of the simulation and these patterns are dominated spatially and energetically by azimuthal Fourier modes with frequencies of 2 and 3. Studies of the transition between these two large-scale patterns, radial and vertical variations in the azimuthal energy spectra, as well as the spatial and modal variations in the system's correlation time are conducted. Rotational dynamics are observed for individual Fourier modes and the global structure with strong similarities to the dynamics that have been reported for unit aspect-ratio domains in prior works. It is shown that the large-scale structures have very long correlation time scales, on the order of hundreds to thousands of free-fall time units, and that they are the primary source for a horizontal inhomogeneity within the system that can be observed during a finite, but a very long-time simulation or experiment.

Laboratory experiments and direct numerical simulations are employed to investigate lock-exchange gravity currents propagating over close-packed, fixed porous beds of monodisperse spherical particles, and to quantify the mass and momentum transfer between the currents and the bed. The simulations show that the mass exchange of the current with the bed involves two separate steps that operate on different time scales. In a first step, the dense current front rapidly sweeps away the resident fluid in the exposed pore spaces between the top layer of spheres, while in a second step, a buoyancy-driven vertical exchange flow between the current and the deeper pores is set up that takes significantly longer to develop. This process depends on the permeability of the bed, which in turn is a function of the particle diameter. The momentum exchange between the current and the bed strongly depends on the ratio of the particle size to the viscous sublayer of the current. The bottom friction is moderate when the particle size is smaller than or comparable to the thickness of the viscous sublayer, but it jumps for particles that strongly protrude from the sublayer, leading to a more rapid deceleration of the flow.

This study investigates the transient loading exerted on rigid circular cylinders by impinging pressure waves of arbitrary shape, amplitude and time duration. Numerical calculations are used to predict the transient flow around the cylinder for wide ranges of geometric and loading parameters. An analytical model is developed to predict the transient loading history on the cylinder and this is found to be in good agreement with the results of the numerical calculations. Both models are used to identify and explore the different loading regimes, and to construct non-dimensional maps to allow direct application of the findings of this study to the design of structures exposed to the threat of pressure wave loading.

Lubricant-infused surfaces in an outer liquid flow generally reduce viscous drag. However, owing to the meniscus deformation, the infused state could collapse. Here, we discuss the transition between infused and collapsed states of transverse shallow grooves, considering the capillary number, liquid/lubricant viscosity ratio and the aspect ratio of the groove as parameters for inducing this transition. It is found that, depending on the depth of the grooves, two different scenarios occur. A collapse of lubricant-infused surfaces could happen due to a depinning of the meniscus from the front groove edge. However, for very shallow textures, the meniscus contacts the bottom wall before such a depinning could occur. Our interpretation could help avoid this generally detrimental effect in various applications.