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.

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.

The presence of salt in seawater strongly affects the melt rate and the shape evolution of ice, both of utmost relevance in ice–ocean interactions and thus for the climate. To get a better quantitative understanding of the physical mechanics at play in ice melting in salty water, we numerically investigate the lateral melting of an ice block in stably stratified saline water. The developing ice shape from our numerical results shows good agreement with the experiments and theory from Huppert & Turner (J. Fluid Mech., vol. 100, 1980, pp. 367–384). Furthermore, we find that the melt rate of ice depends non-monotonically on the mean ambient salinity: it first decreases for increasing salt concentration until a local minimum is attained, and then increases again. This non-monotonic behaviour of the ice melt rate is due to the competition among salinity-driven buoyancy, temperature-driven buoyancy and salinity-induced stratification. We develop a theoretical model based on the force balance which gives a prediction of the salt concentration for which the melt rate is minimal, and is consistent with our data. Our findings give insight into the interplay between phase transitions and double-diffusive convective flows.

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 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.

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.

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.

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.

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.