Mixing of fluids in a coaxial jet is studied under four distinct viscosity ratios, $m=1$, $10$, $20$ and $40$, using highly resolved large-eddy simulations (LES), particle image velocimetry and planar laser-induced fluorescence. The accuracy of predictions is tested against data obtained by the simultaneous experimental measurements of velocity and concentration fields. For the highest and lowest viscosity ratios, standard RANS models with unclosed terms pertaining to viscosity variations are employed. We show that the standard Reynolds-averaged Navier–Stokes (RANS) approach with no explicit modelling for variable-viscosity terms is not applicable whereas dynamic LES models provide high-quality agreement with the measurements. To identify the underlying mixing physics and sources of discrepancy in RANS predictions, two distinct mixing modes are defined based on the viscosity ratio. Then, for each mode, the evolution of mixing structures, momentum budget analysis with emphasis on variable-viscosity terms, analysis of the turbulent activity and decay of turbulence are investigated using highly resolved LES data. The mixing dynamics is found to be quite distinct in each mixing mode. Variable viscosity manifests multiple effects that are working against each other. Viscosity gradients induce additional instabilities while increasing overall viscosity decreases the effective Reynolds number leading to laminarization of the turbulent jet, explaining the lack of dispersion and turbulent diffusion. Momentum budget analysis reveals that variable-viscosity terms are significant to be neglected. The scaling of the energy spectrum cascade suggests that in the TLL mode the unsteady laminar shedding is responsible for the eddies observed.

We study the effect of insoluble surfactants on the spatio-temporal evolution of turbulent jets. We use three-dimensional numerical simulations and employ an interface-tracking/level-set method that accounts for surfactant-induced Marangoni stresses. The present study builds on our previous work (Constante-Amores et al., J. Fluid Mech., vol. 922, 2021, A6) in which we examined in detail the vortex–surface interaction in the absence of surfactants. Numerical solutions are obtained for a wide range of Weber and elasticity numbers in which vorticity production is generated by surface deformation and surfactant-induced Marangoni stresses. The present work demonstrates, for the first time, the crucial role of Marangoni stresses, brought about by surfactant concentration gradients, in the formation of coherent, hairpin-like vortex structures. These structures have a profound influence on the development of the three-dimensional interfacial dynamics. We also present theoretical expressions for the mechanisms that influence the rate of production of circulation in the presence of surfactants for a general, three-dimensional, two-phase flow, and highlight the dominant contribution of surfactant-induced Marangoni stresses.

Active diffusion of substances in binary immiscible and incompressible fluids with different densities occurs universally in nature and industry, but relevant mathematical models and numerical simulation have been studied scarcely so far. In this paper, a thermodynamically consistent phase-field model is established to describe the activated solute transport in binary fluids with different densities. A mixed free-energy function for multiple solutes is proposed, which leads to different solute chemical potentials in binary solvent fluids, thus it has the ability to characterize the solubility difference of the solutes in two solvents. The two-phase flow is governed by a general hydrodynamic phase-field model that can account for general average velocity and different densities. The proposed model is derived rigorously using the second law of thermodynamics. Moreover, a general multi-component solute diffusion model is established using the Maxwell–Stefan approach, which involves the crossing influences between different solutes. To solve the model effectively, an efficient, linearized and decoupled numerical method is proposed for the model as well. The proposed numerical method can preserve the thermodynamical consistency, i.e. obeying an energy dissipation law at the discrete level, as well as guarantee the mass conservation law for the solutes and solvent fluids. Numerical experiments are carried out to show that the proposed model and numerical method can simulate various processes of the solute active diffusion in two-phase solvent fluids.

When a cylinder is mounted on an elastic support within a current, vortex-induced vibrations (VIV) may occur down to a Reynolds number (Re) close to $20$, based on the body diameter ($D$) and inflow velocity ($U$), i.e. below the critical value of $47$ reported for the onset of flow unsteadiness when the body is fixed. The impact of a forced rotation of the elastically mounted cylinder on the system behaviour is explored numerically for $Re \leqslant 30$, over wide ranges of values of the rotation rate (ratio between body surface velocity and $U$, $\alpha \in [0,5]$) and reduced velocity (inverse of the oscillator natural frequency non-dimensionalized by $D$ and $U$, $U^\star \in [2,30]$). The influence of the rotation is not monotonic, but the most prominent effect uncovered in this work is a substantial enhancement of the subcritical-Re, flow-induced vibrations beyond $\alpha =2$. This enhancement is twofold. First, the rotation results in a considerable expansion of the vibration/flow unsteadiness region in the $({Re},U^\star )$ domain, down to $Re=4$. Second, the elliptical orbits described by the rotating body are subjected to a major amplification, with a transition from VIV to responses whose magnitude tends to increase unboundedly with $U^\star$, even though still synchronized with flow unsteadiness. The emergence of such galloping-like oscillations close to the onset of vibrations disrupts the scenario of gradual vibration growth with Re, as amplitudes larger than $10$ body diameters may be observed at $Re=10$.

Shock-induced instability developments of two successive interfaces have attracted much attention, but remain a difficult problem to solve. The feedthrough and reverberating waves between two successive interfaces significantly influence the hydrodynamic instabilities of the two interfaces. The evolutions of two successive slow/fast interfaces driven by a weak shock wave are examined experimentally and numerically. First, a general one-dimensional theory is established to describe the movements of the two interfaces by studying the rarefaction waves reflected between the two interfaces. Second, an analytical, linear model is established by considering the arbitrary wavenumber and phase combinations and compressibility to quantify the feedthrough effect on the Richtmyer–Meshkov instability (RMI) of two successive slow/fast interfaces. The feedthrough significantly influences the RMI of the two interfaces, and even leads to abnormal RMI (i.e. phase reversal of a shocked slow/fast interface is inhibited) which is the first observational evidence of the abnormal RMI provided by the present study. Moreover, the stretching effect and short-time Rayleigh–Taylor instability or Rayleigh–Taylor stabilisation imposed by the rarefaction waves on the two interfaces are quantified considering the two interfaces’ phase reversal. The conditions and outcomes of the freeze-out and abnormal RMI caused by the feedthrough are summarised based on the theoretical model and numerical simulation. A specific requirement for the simultaneously freeze-out of the instability of the two interfaces is proposed, which can potentially be used in the applications to suppress the hydrodynamic instabilities.

Recent works on wall-bounded flows have corroborated the coexistence of wall-attached eddies, whose statistical features are predicted through Townsend's attached-eddy hypothesis (AEH), and very-large-scale motions (VLSMs). Furthermore, it has been shown that the presence of wall-attached eddies within the logarithmic layer is linked to the appearance of an inverse-power-law region in the streamwise velocity energy spectra, upon significant separation between outer and viscous scales. In this work, a near-neutral atmospheric surface layer is probed with wind light detection and ranging to investigate the contributions to the streamwise velocity energy associated with wall-attached eddies and VLSMs for a very-high-Reynolds-number boundary layer. Energy and linear coherence spectra (LCS) of the streamwise velocity are interrogated to identify the spectral boundaries associated with eddies of different typologies. Inspired by the AEH, an analytical model for the LCS associated with wall-attached eddies is formulated. The experimental results show that the identification of the wall-attached-eddy energy contribution through the analysis of the energy spectra leads to an underestimate of the associated spectral range, maximum height attained and turbulence intensity. This feature is due to the overlap of the energy associated with VLSMs obscuring the inverse-power-law region. The LCS analysis estimates wall-attached eddies with a streamwise/wall-normal ratio of about 14.3 attaining a height of about 30 % of the outer scale of turbulence.

Using the theory of wave turbulence for rapidly rotating incompressible fluids derived by Galtier (Phys. Rev. E, vol. 68, 2003, 015301), we find the locality conditions that the solutions of the kinetic equation must satisfy. We show that the exact anisotropic Kolmogorov–Zakharov spectrum satisfies these conditions, which justifies the existence of this constant (positive) energy flux solution. Although a direct cascade is predicted in the transverse ($\perp$) and parallel ($\parallel$) directions to the rotation axis, we show numerically that in the latter case some triadic interactions can have a negative contribution to the energy flux, while in the former case all interactions contribute to a positive flux. Neglecting the parallel energy flux, we estimate the Kolmogorov constant at $C_K \simeq 0.749$. These results provide theoretical support for recent numerical and experimental studies.

Geophysical mass flows such as debris flows, dense pyroclastic flows and snow avalanches can self-channelize on shallow slopes. The confinement afforded by formed levees helps to maintain the flow depth, and hence mobility, allowing self-channelized flows to run out significantly farther than unconfined, spreading flows. Levee formation and self-channelization are strongly associated with particle-size segregation, but can also occur in monodisperse flows. This paper uses the monodisperse depth-averaged theory of Rocha et al. (J. Fluid Mech., vol. 876, 2019, pp. 591–641), which incorporates a hysteretic friction law and second-order depth-averaged viscous terms. Both of these are vital for the formation of a travelling wave that progressively deposits a pair of levees just behind the front. The three-dimensional velocity field is reconstructed in a frame moving with the front assuming Bagnold flow. This enables a bidisperse particle-size segregation theory to be used to solve for the large and small particle concentrations and particle paths in three-dimensions, for the first time. The model shows that the large particles tend to segregate to the surface of the flow, forming a carapace that extends over the centre of the channel, as well as along the external sides and base of the levee walls. The small particles segregate downwards, and are concentrated in the main channel and in the inner levee walls. This supports the contention that a low-friction channel lining provides a secondary mechanism for run-out enhancement. It is also shown that the entire theory scales with particle diameter, so experiments with millimetre-sized particles provide important insights into geophysical-scale flows with boulders and smaller rock fragments. The model shows that self-channelization does not need particle-size segregation to occur, but supports the hypothesis that particle-size segregation and the associated frictional feedback can significantly enhance both the flow mobility and the levee strength.

Reliable prediction of the erosion rate of sediment beds is important for many applications in coastal and river engineering. Theoretical understanding of empirically derived scaling relations is still lacking. This applies in particular for the scaling anomaly between low and high Shields number conditions. In this work, the erosion process is studied from the perspective of the phase-averaged turbulent kinetic energy (TKE) equations. The multi-phase TKE equations are written in a form that allows for a direct comparison with the TKE equation that appears for a stratified single-phase flow under the Boussinesq approximation. This reveals that next to buoyancy destruction, several other TKE modulation mechanisms become important at high Shields numbers and concentrations. Two scaling laws are derived for both moderate and high Shields numbers, and are tested against a wide range of experimental data.

We show that a vertical viscosity stratification at a localized region caused by a chemical reaction yields an inconspicuous shear layer. A chemo-hydrodynamic Kelvin–Helmholtz instability or cat-eye-shaped morphology develops at one reaction front, while the other front diffuses steadily over time. Through linear stability and nonlinear simulations, the existence of such instabilities is established if the log-mobility ratio exceeds a critical value. We find unique scalings between the stable and unstable zones that demonstrate how the influence of variations in solute diffusion on instability can be eliminated. The observed unstable patterns agree with existing experimental results.

We propose a novel nonlinear manifold learning from snapshot data and demonstrate its superiority over proper orthogonal decomposition (POD) for shedding-dominated shear flows. Key enablers are isometric feature mapping, Isomap, as encoder and, $K$-nearest neighbours ($K$NN) algorithm as decoder. The proposed technique is applied to numerical and experimental datasets including the fluidic pinball, a swirling jet and the wake behind a couple of tandem cylinders. Analysing the fluidic pinball, the manifold is able to describe the pitchfork bifurcation and the chaotic regime with only three feature coordinates. These coordinates are linked to the vortex-shedding phases and the force coefficients. The manifold coordinates of the swirling jet are comparable to the POD mode amplitudes, yet allow for a more distinct and less noise-sensitive manifold identification. A similar observation is made for the wake of two tandem cylinders. The tandem cylinders are aligned and located at a streamwise distance which corresponds to the transition between the single bluff body and the reattachment regimes of vortex shedding. Isomap unveils these two shedding regimes while the Lissajous plot of the first two POD mode amplitudes features a single circle. The reconstruction error of the manifold model is small compared with the fluctuation level, indicating that the low embedding dimensions contain the coherent structure dynamics. The proposed Isomap–$K$NN manifold learner is expected to be of great importance in estimation, dynamic modelling and control for a large range of configurations with dominant coherent structures.

The fluid–structure interactions between flexible fibres and viscous flows play an essential role in various biological phenomena, medical problems and industrial processes. Of particular interest is the case of particles transported freely in time-dependent flows. This work elucidates the dynamics and morphologies of actin filaments under oscillatory shear flows by combining microfluidic experiments, numerical simulations and theoretical modelling. Our work reveals that, in contrast to steady shear flows, in which small orientational fluctuations from a flow-aligned state initiate tumbling and deformations, the periodic flow reversal allows the filament to explore many different configurations at the beginning of each cycle. Investigation of filament motion during half time periods of oscillation highlights the critical role of the initial filament orientation on the emergent dynamics. This strong coupling between orientation and deformation results in new deformation regimes and novel higher-order buckling modes absent in steady shear flows. The primary outcome of our analysis is the possibility of suppression of buckling instabilities for certain combinations of the oscillation frequency and initial filament orientation, even in very strong flows. We explain this unusual behaviour through a weakly nonlinear Landau theory of buckling, in which we treat the filaments as inextensible Brownian Euler–Bernoulli rods whose hydrodynamics is described by local slender-body theory.

We consider suspensions of finite-size neutrally buoyant rigid spherical particles in channel flow and investigate the relevance of different momentum transfer mechanisms and the relation between the local particle dynamics and the bulk flow properties in the highly inertial regime. Interface-resolved simulations are performed in the range of Reynolds numbers $3000 \leq Re \leq 15\ 000$ and solid volume fractions $0 \leq \phi \leq 0.3$. The Lagrangian particle statistics show that pair interactions are highly inhomogeneous and dependent on the distance from the wall: in their vicinity, the underlying mean shear drives the pair interactions, while a high degree of isotropy, dictated by more frequent collisions, characterizes the core region. Analysis of the momentum balance reveals that while the particle-induced stresses govern the dynamics in dense conditions, $\phi =0.3$, and moderate Reynolds numbers, $Re <10\ 000$, the turbulent stresses take over at higher Reynolds numbers. This behaviour is associated with a reduced particle migration toward the channel core, which decreases the importance of the particle-induced stress and increases the turbulent activity. Our results indicate that Reynolds stresses and the associated velocity fluctuations, characteristics of near-wall turbulence, prevail at high inertia over the resistance to deformation presented by the particles for volume fractions lower than 30 %.

The Rayleigh–Taylor instability at the interface of two sheared fluid layers in a horizontal channel is investigated in the absence of inertia. The dynamics of the flow is described by a nonlinear lubrication equation which is solved numerically for adverse density stratifications. The early-time dynamics features a number of finger-like protrusions of different heights at the interface. The fingers travel at different speeds leading to a sequence of merging events after which the interface eventually settles to a near-saturated state, comprising only one finger that includes most of the lower fluid. For sufficiently large density stratifications, the final state spans the height of the channel and includes two thin fluid films at each wall, both of which undergo chaotic dynamics, but finite-time touch-down/touch-up is shown to be precluded by the shear flow. An asymptotic analysis in the large-Bond-number limit (intense density stratification) reveals the finer structure of the final state including Landau–Levich-type connection regions. The asymptotic solutions are compared with numerical results of the lubrication model as well as direct numerical simulations, and excellent agreement is observed between the three in terms of interfacial structure, wave speed and film thicknesses.

The hydrodynamics of turbulent oscillatory flow over a gravel-based irregular rough wall is investigated using laser-Doppler anemometry measurements of velocities in a large oscillatory flow tunnel and direct numerical simulation (DNS) of the Navier–Stokes equations. The same periodic irregular roughness was used for both experiments and DNS. Four flow shapes are investigated: sinusoidal, skewed, asymmetric and combined skewed–asymmetric. The experiments were conducted for target Reynolds numbers (based on the Stokes length and standard deviation of free-stream velocity) of $R_{\delta,\sigma }=800$ and $R_{\delta,\sigma }=1549$; DNS was conducted for flows with target $R_{\delta,\sigma }=800$. Boundary layer thickness, bottom phase lead and friction factor are in good agreement with previous studies. For the first time, evidence of Prandtl's secondary flows of the second kind in oscillatory flow is presented. Turbulence structure is visualised using isosurfaces of $\lambda _{2}$ (Jeong & Hussain J. Fluid Mech., vol. 285, 1995, pp. 69–94), revealing densely packed structures that grow stronger and weaker in correspondence with the free-stream velocity. Reynolds and dispersive stresses peak just below the highest roughness crest, with dispersive stress vanishing a short distance above the roughness. Bursts of turbulence kinetic energy and wake kinetic energy are generated each flow half-cycle, with variable behaviour depending on flow shape. Non-Gaussian turbulence statistics are observed that originate near the wall, becoming increasingly non-Gaussian far from the wall. Probability density functions of turbulence statistics can be closely approximated by a fourth-order Gram–Charlier distribution at most phases and elevations, though when statistics deviate more strongly from Gaussian, streamwise and wall-normal (spanwise) statistics are better described by a Pearson type IV (VII) distribution.