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.

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.

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.

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.

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.

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.