Enhancing solute dispersion in electrically actuated flows has always been a challenging proposition, as attributed to the inherent uniformity of the flow field in the absence of surface patterns. Over the years, researchers have focused their attention towards circumventing this limitation, by employing several fluidic and geometric modulations. However, the corresponding improvements in solute dispersion often turn out to be inconsequential. Here we reveal that by exploiting the interplay between an externally imposed temperature gradient, subsequent electrical charge redistribution and ionic motion, coupled with the rheological complexities of the fluid, one can achieve enhancement of up to one order of magnitude of solute dispersion in a pressure-driven flow of an electrolyte solution. Our results demonstrate that the complex coupling between thermal, electrical, hydrodynamic and rheological parameters over small scales, responsible for such exclusive phenomenon, can be utilized in designing novel thermally actuated microfluidic and bio-microfluidic devices with favourable solute separation and dispersion characteristics.

We compute the full set of second-order inertial corrections to the instantaneous force and torque acting on a small spherical rigid particle moving unsteadily in a general steady linear flow. This is achieved by using matched asymptotic expansions and formulating the problem in a coordinate system co-moving with the background flow. Effects of unsteadiness and fluid-velocity gradients are assumed to be small, but to dominate in the far field over those of the velocity difference between the body and fluid, making the results essentially relevant to weakly positively or negatively buoyant particles. The outer solution (which at first order is responsible for the Basset–Boussinesq history force at short time and for shear-induced forces such as the Saffman lift force at long time) is expressed via a flow-dependent tensorial kernel. The second-order inner solution brings a number of different contributions to the force and torque. Some are proportional to the relative translational or angular acceleration between the particle and fluid, while others take the form of products of the rotation/strain rate of the background flow and the relative translational or angular velocity between the particle and fluid. Adding the outer and inner contributions, the known added-mass force or the spin-induced lift force are recovered, and new effects involving the velocity gradients of the background flow are revealed. The resulting force and torque equations provide a rational extension of the classical Basset–Boussinesq–Oseen equation incorporating all first- and second-order fluid inertia effects resulting from both unsteadiness and velocity gradients of the carrying flow.

This paper presents the effects of wing kinematics on both normal forward flight and escape flight of a dragonfly. A Navier–Stokes-based numerical model has been adopted, and results have been substantiated by experimental data. The wing kinematics of tethered specimens and the prescribed wing morphology of a free-flying dragonfly were used in the simulation. To shed light on the interplay between kinematics and aerodynamics, a parametric study of the kinematics has been conducted. It is found that in escape flight, the dragonfly generates additional lift while the thrust reduces and the overall efficiency drops. Compared with normal forward flight, the escape mode produces larger lift force peaks. When the kinematics change to facilitate escape flight, the aerodynamic forces are affected by not only the flapping kinematics but, in the case of the hindwing, the varied wing–wing vortex interactions. The direction of the resultant force on each wing changes according to the change of the mean of pitching angle and stroke plane angle. We found that in the studied configurations, the varied phasing of the wings has a marginal effect on the aerodynamics of the dragonfly. It reduces lift and increases thrust, and this force modulation is slightly more efficient when the local angle of attack also changes. On the other hand, the change of angle of attack played a major role in leading-edge vortex formations and directing the resultant forces of the wings. The results can be useful in developing flight control strategies for micro air vehicle design.

The propagation of dam-break waves on different rough beds was observed to be quasi-steady in the range $11.3 < x/h_{dam} < 18.8$, where $x$ is measured from the dam position. These quasi-steady propagation speeds converge with the steady ideal fluids model of Stoker (Water Waves, 1957, Interscience) when the tailwater depth $h_2$ becomes greater than ${\sim }0.5k_s$, in the range $0.001< k_s/h_{dam}< 0.2$, where $k_s$ is the roughness and $h_{dam}$ the depth behind the dam. Hence, this convergence encourages the use of Stoker's steady, ideal fluid solution to develop more general models, including friction effects due to bed roughness and/or viscosity. The new experimental data support a MacLaurin series for the celerity $c$, in analogy with the series in terms of $\sqrt [4]{{h_2}/{h_{dam}}}$, derived for Stoker's model, $h_2$ being the tailwater depth. Compared with the retarding effect of the tailwater, 1 mm of roughness is found to be equivalent to $\sim$13 mm of tailwater, and 1 $\mathrm {\mu }$m of viscous length (${\nu }/{\sqrt {gh_{dam}}}$, where ${\nu}$ is the kinematic viscosity and g the acceleration due to gravity) is equivalent to $\sim$1700 $\mathrm {\mu }$m of tailwater. While the MacLaurin series quantifies the similar effects of small roughness and small tailwater depths acting separately, the new data illustrate for the first time the complex interplay between tailwater and roughness on ‘wet beds’ with many details yet to be investigated. In particular, it was shown that a small amount of tailwater on a rough bed acts as a lubricant, so that $c(h_2, h_{dam}, k_s)$ is an increasing function of $h_2$ for $h_2 < 0.5k_s$.

This work describes the application of a technique that extracts branched manifolds from time series to study numerically generated fluid particle behaviour in the wake past a cylinder performing a rotary oscillation at low Reynolds numbers, and compares it with the results obtained for a paradigmatic analytical model of Lagrangian motion: the driven double gyre. The approach does not require prior knowledge of the underlying equations defining the dataset. The time series taken as input corresponds to the evolution of a position coordinate of an individual fluid particle. A delay embedding is used to reconstruct the dynamics in phase space, and a cell complex is built to characterize the topology of the embedding. Fluid particles are said to belong to the same topological class when the Betti numbers, orientability chains and weak boundaries of the associated cell complexes coincide. Topological colouring consists of labelling or ‘colouring’ advected particles with the topological class obtained in their finite-time analyses. The results suggest that topological colouring can be used to distinguish between regions of the flow where trajectories exhibit different finite-time dynamics.

Experiments were carried out in high Reynolds number turbulent boundary layers over rough surfaces of diverse geometries. Roughness configurations varied in element height, distribution (random versus ordered), shape and spacing. Rough surfaces comprising of two superposed element geometries were also tested. All flows were free of transitional effects with $Re_{\unicode[STIX]{x1D703}}$ upwards of 40 000 and $\unicode[STIX]{x1D6FF}/k_{g}$ ratios above 73. The wall-pressure spectrum and turbulent velocity profiles revealed that the roughness element spacing has the greatest impact on the turbulent structures in the boundary layer. The high-frequency scaling on shear friction velocity, $U_{\unicode[STIX]{x1D708}}$, (Meyers et al.J. Fluid Mech., vol. 768, 2015, pp. 261–293) was validated and $U_{\unicode[STIX]{x1D708}}$ was shown to be the viscous contribution to the overall surface drag. An empirical formula for the pressure drag on roughness elements was developed to reflect the finding that the pressure drag is a function of only two variables: sparseness ratio $(\unicode[STIX]{x1D706})$ and roughness Reynolds number $(k_{g}^{+})$. Results also suggest that the viscous contribution to drag approaches a constant non-zero value at high Reynolds numbers, and ‘fully rough-wall flow’ may occur at higher $k_{g}^{+}$ than previously thought.

Liquid metal flows, generated in a cylindrical cell by a strong electric current flowing from the central bottom electrode to the sidewall, are studied experimentally and numerically. In the absence of an external magnetic field, the flow is caused by the interaction of the electric current with its own magnetic field and is known as electro-vortex flows (EVF), which has a pure poloidal configuration. It is also well known that even a relatively weak azimuthal force (which immediately arises if a vertical external magnetic field is applied) induces a swirl that completely changes the structure of the flow, suppressing the poloidal motion (Davidson et al., Eur. J. Mech. B Fluids, vol. 18, 1999, pp. 693–711). We study the steady-state modes and analyse the dynamics of transient modes, following the evolution of the flow structure at different ratios of azimuthal and poloidal Lorentz forces, governed by the applied current and vertical magnetic field. In the considered problem, the peculiarities of transient modes, leading to the suppression of the poloidal flow, are associated with the fact that the domain of acting forces is localized in the vicinity of the bottom electrode. The scenario of flow evolution strongly depends on the ratio of electro-vortex and rotational forces (whether the EVF has time to form before a noticeable swirl of the metal, or the swirl dominates from the beginning of flow evolution).

This paper provides a comprehensive explanation for the lift force acting on a freely deformable bubble rising in a linear shear flow and examines how the lift force scales with the undisturbed shear rate in cases governed by different lift force mechanisms. Four distinct flow mechanisms are identified from previous studies, and the associated bubble-induced vorticity dynamics are outlined. We provide a theoretical framework to qualitatively explain the lift force acting on a bubble in terms of moments of the bubble-induced vorticity. We support our theoretical framework with three-dimensional multiphase direct numerical simulations to illustrate how the vorticity dynamics associated with the four mechanisms generate the lift force. These findings provide a comprehensive explanation for the behaviour of the lift force in a wide range of relevant governing parameters. Additionally, our simulation results show how differently the lift force scales with the shear rate, depending on the dominating lift force mechanism. These results indicate that the shear rate should, in general, be accounted for in highly viscous flows (low Galilei numbers) or at significant bubble deformations (moderate-to-high Eötvös numbers) when modelling the lift force coefficient.

Transient electrohydrodynamics of a liquid drop at finite Reynolds numbers is studied by computer simulations. The governing equations of the problem are solved using a parallelized front tracking/finite difference method in the framework of the Taylor–Melcher leaky dielectric theory. The effect of the dielectric properties of the fluids on the dynamic response of the drop is studied by considering three representative fluid systems, which encompass all the regions of the deformation–circulation map. A parametric study is performed over a range of capillary number $Ca$, the Ohnesorge number squared $Oh^{2}$ and the viscosity ratio $\widetilde{\unicode[STIX]{x1D707}}$ to explore the effect of these parameters on the dynamic response. At low to intermediate capillary numbers, the dynamic response resembles that of a first- or second-order mechanical system, where the deformation settles to a steady state monotonically or through oscillations. However, beyond a threshold capillary number, the dynamic response becomes nonlinear. It is shown that the Ohnesorge number squared $Oh^{2}$ and the viscosity ratio $\widetilde{\unicode[STIX]{x1D707}}$ are the key parameters that determine the transition from a monotonic response to an oscillatory one (and vice versa) in density-matched fluid systems. To predict the dynamic response of nearly spherical drops at arbitrary $Oh^{2}$, an analytical equation is developed, which results in a critical Ohnesorge number squared $Oh_{c}^{2}$ that demarks a monotonic response from an oscillatory one. Investigations on the effect of the viscosity ratio $\widetilde{\unicode[STIX]{x1D707}}$ on the dynamic response shows that the relaxation time (for monotonic response) increases with an increase in $\widetilde{\unicode[STIX]{x1D707}}$ and that the steady state deformation ${\mathcal{D}}_{ss}$ correlates positively with $\widetilde{\unicode[STIX]{x1D707}}$ for oblate drops; however, depending on the corresponding regions of prolate drops on the deformation–circulation map, ${\mathcal{D}}_{ss}$ correlates positively or negatively with $\widetilde{\unicode[STIX]{x1D707}}$. A long-standing misconception regarding the oblate region is also rectified by development of a normal stress map, which determines the relative importance of the electric pressure and the normal hydrodynamic stress in setting the sense of the deformation of the drop.

We employ a recently introduced structured input–output analysis (SIOA) approach to analyse streamwise and spanwise wavelengths of flow structures in stably stratified plane Couette flow. In the low-Reynolds-number ($Re$) low-bulk Richardson number ($Ri_b$) spatially intermittent regime, we demonstrate that SIOA predicts high amplification associated with wavelengths corresponding to the characteristic oblique turbulent bands in this regime. SIOA also identifies quasi-horizontal flow structures resembling the turbulent–laminar layers commonly observed in the high-$Re$ high-$Ri_b$ intermittent regime. An SIOA across a range of $Ri_b$ and $Re$ values suggests that the classical Miles–Howard stability criterion ($Ri_b\leq 1/4$) is associated with a change in the most amplified flow structures when the Prandtl number is close to one ($Pr\approx 1$). However, for $Pr\ll 1$, the most amplified flow structures are determined by the product $PrRi_b$. For $Pr\gg 1$, SIOA identifies another quasi-horizontal flow structure that we show is principally associated with density perturbations. We further demonstrate the dominance of this density-associated flow structure in the high $Pr$ limit by constructing analytical scaling arguments for the amplification in terms of $Re$ and $Pr$ under the assumptions of unstratified flow (with $Ri_b=0$) and streamwise invariance.

In the present study, turbulent particle-laden boundary layer combustion over a flat plate is investigated using direct numerical simulation (DNS). A two-way coupled Eulerian–Lagrangian point particle method is used for the solid phase. The effects of particle Stokes numbers, mass loadings and chemical reactions on the interactions between particles and boundary layer turbulence in the near-wall region are explored. It was found that particle heat transfer is dominant over wall heat transfer in the reacting case with heavy particles and large mass loadings, resulting in a lower fluid temperature. Particle accumulation due to the turbophoresis effect in the near-wall region is observed, which is more prominent in the cases with a large Stokes number. The turbophoresis effect is examined via the magnitude of streamwise vorticity $\varOmega _x$. It is shown that $\varOmega _x$ is attenuated by heavy particles, and the attenuation increases with increasing mass loadings. Therefore, particle wall–accumulation is less prominent in the cases with large mass loadings. Compared with the non-reacting cases, the distribution of particles is more inhomogeneous for the reacting cases, where the particles move faster due to intense reactions with increasing wall-normal distance. Finally, the flow topologies and the Reynolds stress anisotropy are examined to understand turbulence modulation by combustion and particles. It was suggested that light particles augment the vortex-dominant topologies, whereas heavy particles have an opposite effect. The anisotropy mapping of the Reynolds stress shows that the flows become more one-dimensional in the near-wall region for the cases with combustion and/or large mass loadings.

We found a multi-scale steady solution of the Boussinesq equations for Rayleigh–Bénard convection in a three-dimensional periodic domain between horizontal plates with a constant temperature difference. This was realised using a homotopy from the wall-to-wall optimal transport solution provided by Motoki et al. (J. Fluid Mech., vol. 851, 2018, R4). A connected steady solution, which is a consequence of bifurcation from a thermal conduction state at Rayleigh number $Ra\sim 10^{3}$, is tracked up to $Ra\sim 10^{7}$ using a Newton–Krylov iteration. The three-dimensional exact coherent thermal convection exhibits a scaling of $Nu\sim Ra^{0.31}$ (where $Nu$ is the Nusselt number) as well as multi-scale thermal plume and vortex structures, which are quite similar to those in turbulent Rayleigh–Bénard convection. The mean temperature profiles and the root-mean-square of the temperature and velocity fluctuations are in good agreement with those of the turbulent states. Furthermore, the energy spectrum follows Kolmogorov's $-5/3$ scaling law with a consistent prefactor, and the energy transfer to small scales with a nearly constant flux in the wavenumber space is in accordance with the turbulent energy transfer.

Large-eddy simulation (LES) of a wind- and wave-forced water column based on the Craik–Leibovich (C–L) vortex force is used to understand the structure of small-scale Langmuir circulation (LC) and associated Langmuir turbulence. The LES also serves to understand the role of the turbulence in determining molecular diffusive scalar flux from a scalar-saturated air side to the water side and the turbulent vertical scalar flux in the water side. Previous laboratory experiments have revealed that small-scale LC beneath an initially quiescent air–water interface appears shortly after the initiation of wind-driven gravity–capillary waves and provides the laminar–turbulent transition in wind speeds between 3 and $6~\text{m}~\text{s}^{-1}$. The LES reveals Langmuir turbulence characterized by multiple scales ranging from small bursting eddies at the surface that coalesce to give rise to larger (centimetre-scale) LC over time. It is observed that the smaller scales account for the bulk of the near-surface turbulent vertical scalar flux. Although the contribution of the larger (centimetre-scale) LC to the near-surface turbulent flux increases over time as these scales emerge and become more coherent, the contribution of the smaller scales remains dominant. The growing LC scales lead to increased vertical scalar transport at depths below the interface and thus greater scalar transfer efficiency. Simulations were performed with a fixed wind stress corresponding to a $5~\text{m}~\text{s}^{-1}$ wind speed but with different wave parameters (wavelength and amplitude) in the C–L vortex force. It is observed that longer wavelengths lead to more coherent, larger centimetre-scale LC providing greater contribution to the turbulent vertical scalar flux away from the surface. In all cases, the molecular diffusive scalar flux at the water surface relaxes to the same statistically steady value after transition to Langmuir turbulence occurs, despite the different wave parameters in the C–L vortex force across the simulations. This implies that the small-scale turbulence intensity and the molecular diffusive scalar flux at the surface scale with the wind shear and not with the wave parameters. Furthermore, it is seen that the Langmuir (wave) forcing (provided by the C–L vortex force) is necessary to trigger the turbulence that induces elevated molecular diffusive scalar flux at the water surface relative to wind-driven flow without wave forcing.

The structure of the steady boundary layer in the airflow over young wind waves is studied in detail using extensive data accumulated in our laboratory as well as in additional laboratory facilities and in field measurements. Following the approach adopted in studies of turbulent flow over solid rough surfaces, the coupling between the spatial evolution of wind waves and wind velocity profiles over the water is analysed. The roughness of the moving water surface under wind is not constant; wind waves that constitute the roughness elements are unsteady, random and three-dimensional. The effective water surface roughness increases with airflow velocity as well as with downstream distance. Nevertheless, the existence of wall similarity as observed in a flow over solid surfaces is demonstrated; a fully rough boundary layer is obtained for young wind waves at diverse operational conditions. This approach enables quantitative study of the coupling between the airflow and local wind wave characteristics.