Turbulent shear flows are abundant in geophysical and astrophysical systems and in engineering-technology applications. They are often riddled with large-scale secondary flows that drastically modify the characteristics of the primary stream, preventing or enhancing mixing, mass and heat transfer. Using experiments and numerical simulations, we study the possibility of modifying these secondary flows by using superhydrophobic surface treatments that reduce the local shear. We focus on the canonical problem of Taylor–Couette flow, the flow between two coaxial and independently rotating cylinders, which has robust secondary structures called Taylor rolls that persist even at significant levels of turbulence. We generate these structures by rotating only the inner cylinder of the system, and show that an axially spaced superhydrophobic treatment can weaken the rolls through a mismatching surface heterogeneity, as long as the roll size can be fixed. The minimum hydrophobicity of the treatment required for this flow control is rationalized, and its effectiveness beyond the Reynolds numbers studied here is also discussed.

We present the results of a combined experimental and theoretical investigation of sheet evolution, expansion and retraction, under unsteady fragmentation upon drop impact on a surface of comparable size to that of the drop. We quantify and model the effect of the continuous time-varying – unsteady – shedding of droplets from the sheet via its bounding rim. We present and validate especially developed advanced image processing algorithms that quantify, with high accuracy, the key quantities involved in such unsteady fragmentation, from sheet, to rim, to ligaments, to droplet properties. With these high precision measurements, we show the important effect of continuous unsteady droplet shedding on the sheet dynamics. We combine experiments and theory to derive and validate governing equations of the sheet that incorporate such continuous shedding – associated with continuous loss of momentum and mass – from unsteady fragmentation. Combining this theory with the universal unsteady rim dynamics discovered in Wang et al. (Phys. Rev. Lett., vol. 120, 2018, 204503), we show that the governing equation of the sheet can be reduced to a continuous-shedding, non-Galilean Taylor–Culick law, from which we deduce new analytical expressions for the time evolution of the sheet radius. We show the robustness of the predictions to changes of fluid properties, including surface tension and moderate fluid viscosity and elasticity, including use of physiological mucosalivary fluid. We also reconcile prior literature's inconsistent experimental results on the sheet dynamics upon drop impact.

The stratified inclined duct (SID) experiment consists of a zero-net-volume exchange flow in a long tilted rectangular duct, which allows the study of realistic stratified shear flows with sustained internal forcing. We present the first three-dimensional direct numerical simulations (DNS) of SID to explore the transitions between increasingly turbulent flow regimes first described by Meyer & Linden (J. Fluid Mech., vol. 753, 2014, pp. 242–253). We develop a numerical set-up that faithfully reproduces the experiments and sustains the flow for arbitrarily long times at minimal computational cost. We recover the four qualitative flow regimes found experimentally in the same regions of parameter space: laminar flow, waves, intermittent turbulence and fully developed turbulence. We find good qualitative and quantitative agreement between DNS and experiments and highlight the added value of DNS to complement experimental diagnostics and increase our understanding of the transition to turbulence, both temporally (laminar/turbulent cycles) and parametrically (as the tilt angle of the duct and the Reynolds number are increased). These results demonstrate that numerical studies of SID – and deeper integration between simulations and experiments – have the potential to lead to a better understanding of stratified turbulence.

This study examines the two-dimensional interaction of two unequal co-rotating viscous vortices in uniform background shear. Numerical simulations are performed for vortex pairs having various circulation ratios $\varLambda _0 = \varGamma _{1,0}/\varGamma _{2,0} = (\omega _{1,0}/\omega _{2,0})(a^2_{1,0}/a^2_{2,0}) \leqslant 1$, corresponding to different initial characteristic radii $a_{i,0}$ and peak vorticities $\omega _{i,0}$ of each vortex $i=1,2$, in shears of various strengths $\zeta _0 = \omega _S/\omega _{2,0}$, where $\omega _S$ is the constant vorticity of the shear. Two primary flow regimes are observed: separations ($\zeta _0 < \zeta _{sep} < 0$), in which the vortices move apart continuously, and henditions ($\zeta _0 > \zeta _{sep}$), in which the interaction results in a single vortex (where $\zeta _{sep}$ is the adverse shear strength beyond which separation occurs). Vortex motion and values of $\zeta _{sep}(\varLambda _0)$ are well-predicted by a point-vortex model for unequal vortices. In vortex-dominated henditions, shear varies the peak–peak distance $b$, and vortex deformation. The main convective interaction begins when core detrainment of one vortex is established, and proceeds similarly to the no-shear ($\zeta _0 = 0$) case: merger occurs if the second vortex also detrains, engendering mutual entrainment; otherwise straining out occurs. Detrainment requires persistence of straining of both sufficient magnitude, as indicated by relative straining above a consistent critical value, $(S/\omega )_i > (S/\omega )_{cr}$, where $S$ is the strain rate magnitude at the vorticity peak, and conducive direction. Hendition outcomes are assessed in terms of an enhancement factor $\varepsilon \equiv \varGamma _{end}/\varGamma _{2,start}$. Although $\varepsilon$ generally varies with $\zeta _0$, $(a^2_{1,0} /a^2_{2,0} )$ and $(\omega _{1,0}/\omega _{2,0})$ in a complicated manner, this variation is well-characterized by the pair's starting enstrophy ratio, $Z_2/Z_1$. Within a transition region between merger and straining out (approximately $1.65 < Z_2/Z_1 < 1.9$), shear of either sense may increase $\varepsilon$.

Effects of the spanwise wavelength (λ) of a sinusoidal wavy cylinder with elliptic cross-section on wake structures and fluid forces are numerically investigated at a Reynolds number Re = 100. A wide range of the wavelength, $0.43 \le \lambda /{D_m} \le 8.59$, is considered with a wave amplitude of a/Dm = 0.048, where Dm is the hydraulic diameter of the wavy cylinder. Based on vortical structures, Strouhal number (St) and wake closure length (Lc), fluid forces, streamline topologies and spatio-temporal evolutions of the near wake, five distinct flow patterns (I–V) are identified depending on λ/Dm. The drag force reaches its minimum in pattern III, the fluctuating lift force is zero in flow patterns III and IV. Distinct from the classical flow where alternate vortex shedding occurs synchronously over the entire cylinder span, flow pattern IV has alternate vortex shedding over a one half-wavelength of the wavy elliptic cylinder, antiphased with that over the other half-wavelength, thus leading to zero fluctuating lift over one complete wavelength. A thorough comparison of the wakes is made between the wavy elliptic cylinder and wavy circular or square cylinder, distinguishing the underlying flow physics behind the salient behaviours observed.

Large-eddy simulation on a grid consisting of 5 billion points was utilized to study the properties of turbulence at the core of the tip and hub vortices shed by a marine propeller across working conditions. Turbulence at the core of the tip vortices was found to be initially isotropic, moving towards a ‘cigar-shaped’ axisymmetric state as instability grows, dominated by turbulent fluctuations of the velocity component directed in the radial direction of the cylindrical reference frame centred at the wake axis. The break-up of the coherence of the tip vortices is instead characterized by turbulence recovering an isotropic state. This process is accelerated by growing load conditions of the propeller. In contrast, during instability of the hub vortex, turbulence at its core develops a ‘pancake-shaped’ axisymmetric state, dominated by the fluctuations of the radial and azimuthal velocities. However, at higher propeller loads turbulence at the core of the hub vortex keeps close to isotropy, thanks to a faster instability. Within both tip and hub vortices the deviations from Boussinesq's hypothesis were found very significant, providing evidence of the unsuitability of conventional turbulence modelling. At the core of the tip vortices they become especially large at their break-up and for increasing load conditions of the propeller, equivalent to more intense structures. In contrast, at the core of the hub vortex they were verified to be decreasing functions of the propeller load.

Polymers in a turbulent flow are stretched out by the fluctuating velocity gradient and exhibit a broad distribution of extensions $R$; the stationary probability density function (p.d.f.) of $R$ has a power-law tail with an exponent that increases with the Weissenberg number $\mathit {Wi}$, a non-dimensional measure of polymer elasticity. This study addresses the following questions. (i) What is the role of the non-Gaussian statistics of the turbulent velocity gradient on polymer stretching? (ii) How does the p.d.f. of $R$ evolve to its asymptotic stationary form? Our analysis is based on simulations of the dynamics of finitely extensible bead–spring dumbbells and chains, in the extremely dilute limit, that are transported in a homogeneous and isotropic turbulent flow, as well as in a Gaussian random flow. We show that while the turbulent flow is more effective at stretching small-$\mathit {Wi}$ stiff polymers, the Gaussian flow is more effective for high-$\mathit {Wi}$ polymers. This suggests that high-$\mathit {Wi}$ polymers (with large relaxation times) are stretched primarily by the cumulative effect of moderate strain rate events, rather than by short-lived extreme-valued strain rates. Next, we show that, beginning from a distribution of coiled polymers, the p.d.f. of $R$ exhibits two distinct regimes of evolution. At low to moderate $\mathit {Wi}$, the p.d.f. quickly develops a power-law tail with an exponent that evolves in time and approaches its stationary value exponentially. At high $\mathit {Wi}$, the rapid stretching of polymers first produces a peak in the p.d.f. near their maximum extension; a power law with a constant exponent then emerges and expands its range towards smaller $R$. The time scales of equilibration, measured as a function of $\mathit {Wi}$, point to a critical slowing down at the coil–stretch transition. Importantly, these results show no qualitative change when chains in a turbulent flow are replaced by dumbbells in a Gaussian flow, thereby supporting the use of the latter for reduced-order modelling.

We develop a frame-invariant theory of material spike formation during flow separation over a no-slip boundary in three-dimensional flows with arbitrary time dependence. Based on the exact evolution of the largest principal curvature on near-wall material surfaces, our theory identifies fixed and moving separation. Our approach is effective over short time intervals and admits an instantaneous limit. As a byproduct, we derive explicit formulas for the evolution of the Weingarten map and the principal curvatures of any surface advected by general three-dimensional flows. The material backbone we identify acts first as a precursor and later as the centrepiece of Lagrangian flow separation. We discover previously undetected spiking points and curves where the separation backbones connect to the boundary and provide wall-based analytical formulas for their locations. We illustrate our results on several steady and unsteady flows.

The scalar dispersion of a ground-level point-source plume in a smooth-wall turbulent boundary layer is experimentally investigated using simultaneous particle image velocimetry and planar laser-induced fluorescence techniques. In the near-source region, the viscous sublayer is observed to trap dye, while in the far field, the half-width, vertical profiles and peak decay of the mean concentration and concentration variance exhibit self-similar behaviour and collapse with empirical relations. Full two-dimensional maps of the turbulent scalar fluxes show a net transport direction of upward and towards the incoming flow, with the vertical profiles collapsing well with Weibull-type exponential functions and the decay of peaks following power laws. Using the first-order gradient transport to model the turbulent scalar fluxes, maps of the anisotropic turbulent diffusivity tensor and an effective turbulent diffusivity coefficient are calculated. The streamwise and wall-normal turbulent scalar fluxes are driven dominantly by the wall-normal concentration gradient. The turbulent Schmidt number, relating the turbulent diffusivity and the turbulent (eddy) viscosity calculated using the Boussinesq hypothesis, varies with wall-normal position with values of the order of unity in the logarithmic layer.

Our understanding of the material organization of complex fluid flows has benefited recently from mathematical developments in the theory of objective coherent structures. These methods have provided a wealth of approaches that identify transport barriers in three-dimensional (3-D) turbulent flows. Specifically, theoretical advances have been incorporated into numerical algorithms that extract the most influential advective, diffusive and active barriers to transport from data sets in a frame-indifferent fashion. To date, however, there has been very limited investigation into these objectively defined transport barriers in 3-D unsteady flows with complicated spatiotemporal dynamics. Similarly, no systematic comparison of advective, diffusive and active barriers has been carried out in a 3-D flow with both thermally driven and mechanically modified structures. In our study, we utilize simulations of turbulent rotating Rayleigh–Bénard convection to uncover the interplay between advective transport barriers (Lagrangian coherent structures), material barriers to diffusive heat transport, and objective Eulerian barriers to momentum transport. For a range of (inverse) Rossby numbers, we identify each type of barrier and find intriguing relationships between momentum and heat transport that can be related to changes in the relative influence of mechanical and thermal forces. Further connections between bulk behaviours and structure-specific behaviours are also developed.

In conventional microfluidic devices, fluids are often confined behind solid plastic walls that restrict access and trap gas bubbles; in open microfluidics some solid walls are replaced by fluid ones (i.e. interfaces with immiscible fluids). In both cases, flows are usually driven by external pumps or gravity. An innovative open technology has been developed in which two-dimensional patterns of cell-culture medium in standard Petri dishes are confined by fluid walls made of an immiscible and bio-inert fluorocarbon (FC40). To provide refreshing media flows to cells in such circuits, an established pumping system that exploits differences in Laplace pressure across open interfaces has been applied to drive flow without using external pumps: a source drop autonomously empties through a straight conduit into the rest of the dish (the sink). Whereas conduits with solid walls have unchanging boundaries and flows within them are well understood, the challenge is to predict flows in circuits where fluid walls morph as pressures change. Numerical and semi-analytical equations enabling the prediction of changing flows are developed, and predictions validated experimentally.

Near-wall turbulence structures and generation in the wall-modelled large-eddy simulation (WMLES) are revealed. To elucidate the turbulence structures driving a near-wall turbulence generation in the WMLES, flat-plate turbulent boundary-layer flows calculated by the WMLES and direct numerical simulation (DNS) are closely investigated. A conditional-averaging technique is applied to the instantaneous flow fields and the near-wall statistical structures of the ejection and sweep pairs, which produce the turbulence, are revealed to exist even in the WMLES although the structures are non-physically elongated compared with those obtained by the DNS. Since the near-wall turbulence structures in the WMLES are revealed not to be disordered, but to be coherent structures with low- and high-speed fluids alternating in the spanwise direction, it is suggested that the near-wall turbulence generation in the WMLES is explained by the numerically elongated coherent structures. Furthermore, the Reynolds number effects of wall-bounded turbulent flows, i.e. the appearance of the outer peak in the energy spectrum of the streamwise velocity fluctuations at increasing Reynolds numbers, is found not to be reproduced by the WMLES, and the origin of the outer peak is discussed in association with the inner–outer-layer interactions. The near-wall turbulence structures in the WMLES could depend heavily on the computational grids and the numerical methods. Therefore, additional cases varying the grid resolutions and the numerical methods (numerical schemes and sub-grid-scale models) are also conducted to confirm the consistency of the present conclusions.

Langmuir circulations (LCs) arise through the interaction between the Lagrangian drift of the surface waves and the wind-driven shear layer. Quasi-streamwise vortices (QSVs) also form in the turbulent shear layer next to a flat surface. Both vortical structures manifest themselves by inducing wind-aligned streaks on the surface. In this study, numerical simulations of a stress-driven turbulent shear layer bounded by monochromatic surface waves are conducted to reveal the vortical structures of LCs and QSVs, and their interactions. The LC structure is educed from conditional averaging guided by the signatures of predominant streaks obtained from empirical mode decomposition; the width of the averaged LC pair is found to be comparable to the most unstable wavelength of the Craik–Leibovich equation. Coherent vortical structures (CVSs) are identified using a detection criterion based on local analysis of the velocity-gradient tensor and their topological geometry; QSVs accumulated beneath the windward surface are found to dominate the distribution. Employing the variable-interval spatial average to the identified QSVs further reveals that QSVs tend to form in the edge vicinity of the surface streaks induced by the LCs. The transport budgets of streamwise enstrophy are examined to reveal the interaction. It is found that QSVs perturb the streaks resulting in a localized streamwise gradient of the spanwise velocity, that is, vertical vorticity. The vertical shear tilts the vertical vorticity, therefore enhancing streamwise enstrophy production and the formation of QSVs. The results highlight the differences in the CVSs between the Langmuir turbulence and the wall turbulence.

The roll waves in open-channel flow on steep slopes can strike an obstacle with great force. We conducted two-dimensional shallow-water simulations to study the impact force of the waves against structures of various shapes and orientations. The focus is on the front runner of a wave packet developed from spatial instability. The numerical results include the stand-off distance of the bow shock wave, the front face's run-up height and the wave force on the obstacle. The strength of the impact depends on the Froude number of the undisturbed flow and the obstacle's distance from the local disturbance but not much on the form of the perturbation that initiates the instability. The wave force could reach a peak of more than an order of magnitude greater than the force on the structure without the roll waves. However, an obstacle with a sharp and pointy front can deflect the incident waves, significantly reducing the impact force.

Experiments are conducted in an open-channel flow where half of the section is smooth and the other half consists of an array of cubes, which are either submerged or emergent. A shear layer featuring large-scale Kelvin–Helmholtz structures develops between the two subsections. The flows are first analysed in the framework of the double-averaging method (averaging of the flow both in time and space). Double averaging could be performed thanks to an experimental set-up (three-dimensional, two-component telecentric scanning particle image velocimetry) that allows to measure the velocity field in a large volume, including the interstices between the cubes. A momentum balance performed on the smooth subsection indicates that the loss of momentum towards the rough subsection has the same order of magnitude than the momentum loss through bed friction. This lateral momentum flux occurs nearly exclusively through turbulent shear stress, whereas secondary currents plays a minor role and dispersive shear stress is negligible. A pattern recognition technique is then applied to investigate statistically the large-scale Kelvin–Helmholtz structures that develop in the shear layer. The structures appear to be coherent over the water depth and to be strongly inclined in the vertical, the top part being ahead. The educed coherent structure is responsible by itself for the shape of the velocity profile across the shear layer and for a large part of the turbulence (up to 60 % for the turbulent shear stress). Finally, a coupling is identified between the passage of the Kelvin–Helmholtz structures and the instantaneous wake flow around the cubes at the interface.

The flow-induced snap-through dynamics of a buckled flexible filament was explored using the penalty immersed boundary method. The effects of the filament length, bending rigidity and Reynolds number on the mode transition were systematically examined. Three different modes were observed when the aforementioned parameters were varied: an equilibrium mode, a streamwise oscillation mode and a snap-through oscillation mode. Two mode transitions occurred when the bending rigidity was lowered and the length and Reynolds number were increased: a direct transition from the equilibrium mode to the snap-through oscillation mode and the successive appearance of the three modes. An increase in transverse fluid force induced the snap-through oscillation mode. A vortex-induced vibration and a self-excited vibration occurred in the streamwise oscillation mode and the snap-through oscillation mode, respectively. A wake pattern of 2S appeared in the streamwise oscillation mode, and a pattern of 2S + 2P appeared in the snap-through oscillation mode. A hysteresis was observed near the critical Reynolds number. The hysteresis loop increased in magnitude with increasing bending rigidity. The greater energy harvesting was achieved by the larger deflection and the higher strain energy. We found that most of the strain energy was concentrated in the last half of the filament.

We investigate the hydrodynamics of a spherical and dumbbell-shaped swimmer in a viscoelastic fluid, modelled by the Giesekus constitutive equation. The ‘squirmer’, a model of a micro-swimmer with tangential surface waves at its boundaries, is simulated utilizing a direct-forcing fictitious domain method. We consider the competitive effects of the fluid inertia and elasticity on the locomotion of the swimmers. For the neutral squirmer, its speed increases monotonically with increasing Reynolds number in the Giesekus fluid, in contrast to holding a constant speed in a Newtonian one. Meanwhile, the speed of the finite inertial squirmer increases monotonically with fluid elasticity, as measured by the Weissenberg number. Regarding the dumbbell-shaped swimmers in the Giesekus fluid, we find the pusher–puller (the puller is in front of the pusher) dumbbell swimming to be significantly faster than other dumbbells, providing practical guidance in assembling the complex micro-swimming devices. We further consider the squirmer's (or the dumbbell-shaped squirmer's) energy expenditure and hydrodynamic efficiency, finding that swimming in viscoelastic fluids expends less energy than its Newtonian counterpart, and the neutral squirmer expends more energy than a pusher or puller. The energy expenditure and hydrodynamic efficiency are relevant to steady swimming speeds, in which a faster counterpart squirmer (dumbbell-shaped squirmer) expends less energy but has higher hydrodynamic efficiency.