We present a direct numerical simulation (DNS) study of buoyancy-driven bubbly flows in the presence of large-scale driving that generates turbulence. On increasing the turbulence intensity: (a) the bubble trajectories become more curved and (b) the average rise velocity of the bubbles decreases. We find that the energy spectrum of the flow shows a pseudo-turbulence scaling for length scales smaller than the bubble diameter and a Kolmogorov scaling for scales larger than the bubble diameter. We conduct a scale-by-scale energy budget analysis to understand the scaling behaviour observed in the spectrum. Although our bubbles are weakly buoyant, the statistical properties of our DNS are consistent with the experiments that investigate turbulence modulation by air bubbles in water.

The analysis of turbulence by way of higher-order spectral moments is uncommon, despite the relatively frequent use of such statistical analyses in other fields of physics and engineering. In this work, higher-order spectral moments are used to investigate the internal intermittency of the turbulent velocity and passive-scalar (temperature) fields. This study first introduces the theory behind higher-order spectral moments as they pertain to the field of turbulence. Then, a short-time Fourier-transform-based method is developed to estimate these higher-order spectral moments and provide a relative, scale-by-scale measure of intermittency. Experimental data are subsequently analysed and consist of measurements of homogeneous, isotropic, high-Reynolds-number, passive and active grid turbulence over the Reynolds-number range $35\leq R_{\lambda } \leq ~731$. Emphasis is placed on third- and fourth-order spectral moments using the definitions formalised by Antoni (Mech. Syst. Signal Pr., vol. 20 (2), 2006, pp. 282–307), as such statistics are sensitive to transients and provide insight into deviations from Gaussian behaviour in grid turbulence. The higher-order spectral moments are also used to investigate the Reynolds (Péclet) number dependence of the internal intermittency of velocity and passive-scalar fields. The results demonstrate that the evolution of higher-order spectral moments with Reynolds number is strongly dependent on wavenumber. Finally, the relative levels of internal intermittency of the velocity and passive-scalar fields are compared and a higher level of internal intermittency in the inertial subrange of the scalar field is consistently observed, whereas a similar level of internal intermittency is observed for the velocity and passive-scalar fields for the high-Reynolds-number cases as the Kolmogorov length scale is approached.

We study the evolution of a 2D vortex layer at high Reynolds number. Vortex layer flows are characterized by intense vorticity concentrated around a curve. In addition to their intrinsic interest, vortex layers are relevant configurations because they are regularizations of vortex sheets. In this paper, we consider vortex layers whose thickness is proportional to the square-root of the viscosity. We investigate the typical roll-up process, showing that crucial phases in the initial flow evolution are the formation of stagnation points and recirculation regions. Stretching and folding characterizes the following stage of the dynamics, and we relate these events to the growth of the palinstrophy. The formation of an inner vorticity core, with vorticity intensity growing to infinity for larger Reynolds number, is the final phase of the dynamics. We display the inner core's self-similar structure, with the scale factor depending on the Reynolds number. We reveal the presence of complex singularities in the solutions of Navier–Stokes equations; these singularities approach the real axis with increasing Reynolds number. The comparison between these singularities and the Birkhoff–Rott singularity seems to suggest that vortex layers, in the limit $Re\rightarrow \infty$, behave differently from vortex sheets.

Taylor's hypothesis, or the frozen turbulence approximation, can be used to estimate also the specific energy dissipation rate $\epsilon$ by comparing experimental results with the Kolmogorov–Obukhov expression. The hypothesis assumes that a frequency detected by an instrument moving with a constant large velocity $V$ can be related to a wavenumber by $\omega = k V$. It is, however, not obvious how large the translational velocity has to be in order to make the hypothesis valid, or at least applicable with some acceptable uncertainty. Using the space–time-varying structure function for homogeneous and isotropic conditions, this question is addressed in the present study with emphasis on small velocities $V$. The structure function is obtained using results from numerical solutions of the Navier–Stokes equation. Particular attention is given to the $V$ variation of the estimated specific energy dissipation, $\epsilon _{est}$, compared with the actual value, $\epsilon$, used in the numerical calculations. In contrast to previous studies, the results emphasize velocities $V$ less than or comparable to the one-component root-mean-square velocity, $u_{rms}$. We find that $\epsilon$ can be determined to an acceptable accuracy for $V \geq 0.3\,u_{rms}$. A simple analytical model is suggested to explain the main features of the observations, both Eulerian and Lagrangian. The model assumes that the observed time variations are solely due to eddies moving past the observer, thus ignoring eddy deformation and intermittency effects. In spite of these simplifications, the analysis accounts for most of the numerical results when also eddy-size-dependent velocities are accounted for.

Kinetic energy flux (KEF) is an important physical quantity that characterizes cascades of kinetic energy in turbulent flows. In large-eddy simulation (LES), it is crucial for the subgrid-scale (SGS) model to accurately predict the KEF in turbulence. In this paper, we propose a new eddy-viscosity SGS model constrained by the properly modelled KEF for LES of compressible wall-bounded turbulence. The new methodology has the advantages of both accurate prediction of the KEF and strong numerical stability in LES. We can obtain an approximate KEF by the tensor-diffusivity model, which has a high correlation with the real value. Then, using the artificial neural network method, the local ratios between the real KEF and the approximate KEF are accurately modelled. Consequently, the SGS model can be improved by the product of that ratio and the approximate KEF. In LES of compressible turbulent channel flow, the new model can accurately predict mean velocity profile, turbulence intensities, Reynolds stress, temperature–velocity correlation, etc. Additionally, for the case of a compressible flat-plate boundary layer, the new model can accurately predict some key quantities, including the onset of transitions and transition peaks, the skin-friction coefficient, the mean velocity in the turbulence region, etc., and it can also predict the energy backscatters in turbulence. Furthermore, the proposed model also shows more advantages for coarser grids.

Precession driven flows are of great interest for both, industrial and geophysical applications. While cylindrical, spherical and spheroidal geometries have been investigated in great detail, the numerically and theoretically more challenging case of a non-axisymmetric cavity has received less attention. We report experimental results on the flows in a precessing triaxial ellipsoid, with a focus on the base flow of uniform vorticity, which we show to be in good agreement with existing theoretical models. As predicted, the uniform vorticity component exhibits two branches of solutions leading to a hysteresis cycle as a function of the Poincaré number. The first branch is observed at low forcing and characterized by large amplitude of the total fluid rotation and a moderate tilt angle of the fluid rotation axis. In contrast, the second branch displays only a moderate fluid rotation and a large tilt angle of the fluid rotation axis, which tends to align with the precession axis. In addition, we observe the occurrence of parametric instabilities early in the first branch, which saturate in the second branch, where we observe the same order of the kinetic energy in the base flow and instabilities.

This study describes turbulent flow in a semifilled pipe with a focus on its secondary currents. To the authors’ knowledge, we provide the first highly resolved data-set for semifilled-pipe flow using direct numerical simulation. The flow parameters range from $Re_\tau =115$, just maintaining turbulence, to moderate turbulent flow at $Re_\tau =460$. Some of the main flow characteristics are in line with previously published results from experiments, such as the velocity-dip phenomenon, the main secondary flow and the qualitative distribution of the Reynolds stresses in the core of the flow. We observe some flow phenomena which have not yet been reported in the literature so far for this type of flow. Among those is the inner secondary cell in the mixed corner between the free surface and the pipe's wall, which plays a major role in the distribution of the wall shear stress along the perimeter. We observe that the position and extension of the inner vortex scale with the wall shear stress and those of the outer vortex scale with outer variables. For the first time, we present and discuss distributions of the complete Reynolds stress tensor and its anisotropy which gives rise to the generation of mean streamwise vorticity in a small region in the mixed corners of the pipe. Mean secondary kinetic energy, however, is generated at the free surface around the stagnation point between the inner and outer vortices. This generation mechanism is in line with a vortex dynamics mechanism proposed in the literature.

In this work a mathematical model based on interface energy is proposed within the framework of surface continuum mechanics to study the dynamics of encapsulated bubbles. The interface model naturally induces a residual stress field into the bulk of the bubble, with possible expansion or shrinkage from a stress-free configuration to a natural equilibrium configuration. The significant influence of interface area strain and the coupled effect of stretch and curvature is observed in the numerical simulations based on constrained optimization. Due to the bending rigidity related to additional terms, the dynamic interface tension can become negative, but not due to the interface area strain. The coupled effect of interface strain and curvature term observed is new and plays a dominant role in the dominant compression behaviour of encapsulated bubbles observed in the experiments. The present model is validated by fitting the experimental data of $1.7\,\mathrm {\mu }$m, $1.4\,\mathrm {\mu }$m and $1\,\mathrm {\mu }$m radii bubbles by calculating the optimized parameters. This work also highlights the role of interface parameters and natural configuration gas pressure in estimating the size-independent viscoelastic material properties of encapsulated bubbles with interesting future developments.

We study the topology and the temporal dynamics of turbulent Rayleigh–Bénard convection in a liquid metal with a Prandtl number of 0.03 located inside a box with a square base area and an aspect ratio of $\varGamma = 5$. Experiments and numerical simulations are focused on the Rayleigh number range $6.7 \times 10^{4} \leqslant Ra \leqslant 3.5 \times 10^{5}$, where a new cellular flow regime has been reported previously (Akashi et al., Phys. Rev. Fluids, vol. 4, 2019, 033501). This flow structure shows symmetries with respect to the vertical planes crossing at the centre of the container. The dynamic behaviour is dominated by strong three-dimensional oscillations with a period length that corresponds to the turnover time. Our analysis reveals that the flow structure in the $\varGamma = 5$ box corresponds in key features to the jump rope vortex structure, which has recently been discovered in a $\varGamma = 2$ cylinder (Vogt et al., Proc. Natl Acad. Sci. USA, vol. 115, 2018, pp. 12674–12679). While in the $\varGamma = 2$ cylinder a single jump rope vortex occurs, the coexistence of four recirculating swirls is detected in this study. Their approach to the lid or the bottom of the convection box causes a temporal deceleration of both the horizontal velocity at the respective boundary and the vertical velocity in the bulk, which in turn is reflected in Nusselt number oscillations. The cellular flow regime shows remarkable similarities to properties commonly attributed to turbulent superstructures.

A series of laboratory experiments was conducted to investigate the dynamics of a dense gravity current flowing down an inclined slope into a two-layer stratification in the presence of oncoming internal interfacial waves. The experiment is set up such that the gravity current propagates towards a wave maker emitting interfacial waves such that the current and waves propagate in opposite directions. The results were compared with the case of gravity current without oncoming waves. The gravity current splits into a portion that inserts itself into the pycnocline as an interflow and another that propagates down the slope as an underflow, with the proportionality depending on the characteristics of the gravity current and the oncoming waves when they are present. The interflow is shown to arise from a combination of detrainment and the preferential insertion of fluid with density greater than the upper layer and less than lower layer along the pycnocline. The mass flux of the interflow is observed to be reduced by the oncoming waves, as waves act to decrease the interflow velocity. The internal waves also increase the path length that the interflow must travel. A combination of reduced velocities and increased path length explains the observed reduction in cumulative flux. The trend of the final cumulative flux is consistent with the mass change observed by comparing density profiles obtained before and after the experiment.

Well resolved large-eddy simulation data are used to study the physical modulation effects of miniature vortex generators (MVGs) in a moderate Reynolds number zero pressure gradient turbulent boundary layer. Large-scale counter-rotating primary vortex pairs (PVPs) imposed by the MVG contribute to the formation of streamwise streaks by transporting high momentum fluids from the outer regions of the boundary layer towards the wall, giving rise to high-speed regions centred at the PVP. Consequently, low-speed regions are formed along the outer flank of the PVP, resulting in a pronounced alternating high- and low-speed flow pattern. The PVP also relates to regions with skin friction modification, where a local skin friction reduction of up to 15 % is obtained at the low-speed region, but the opposite situation is observed over the high-speed region. The MVG-induced flow feature is further investigated by spectral analysis of the triple decomposition velocity fluctuation. Pre-multiplied energy spectra of the streamwise MVG-induced velocity fluctuation reveal that the large-scale induced modes scale with the spanwise wavelength and the length of the MVG, but the energy peak is eventually repositioned to the size of the near-wall streaks in the streamwise direction. Analysis of the triple decomposition of the kinetic energy transport equations revealed the significance of the mean flow gradient in generating kinetic energy which sustains the secondary motion. There is also an energy transfer between the turbulent and MVG-induced kinetic energy independent of the mean flow.

The Kármán–Howarth equation (KHEq) is solved using a closure model to obtain solutions of the second-order moment of the velocity increment, $S_2$, in homogeneous isotropic turbulence (HIT). The results are in good agreement with experimental data for decaying turbulence and are also consistent with calculations based on the three-dimensional energy spectrum for decaying HIT. They differ, however, from those for forced HIT, the difference occurring mainly at large scales. This difference is attributed to the fact that the forcing generates large-scale motions which are not compatible with the KHEq. As the Reynolds number increases, the impact of forcing on the small scales decreases, thus allowing the KHEq and spectrally based solutions to agree well in the range of scales unaffected by forcing. Finally, the results show that the two-thirds law is compatible with the KHEq solutions as the Reynolds number increases to very large, if not infinite, values.

The application of drag-control strategies on canonical wall-bounded turbulence, such as periodic channel and zero- or adverse-pressure-gradient boundary layers, raises the question on how to distinguish consistently the origin of control effects under different reference conditions. We employ the RD identity (Renard & Deck, J. Fluid Mech., vol. 790, 2016, pp. 339–367) to decompose the mean friction drag and investigate the control effects of uniform blowing and suction applied to an NACA4412 airfoil at chord Reynolds numbers $Re_c=200\,000$ and $400\,000$. The connection of the drag reduction/increase by using blowing/suction with the turbulence statistics (including viscous dissipation, turbulence kinetic energy production and spatial growth of the flow) across the boundary layer, subjected to adverse or favourable pressure gradients, is examined. We found that the inner and outer peaks of the contributions associated with the friction-drag generation show good scaling with either inner or outer units, respectively. They are also independent of the Reynolds number, control scheme and intensity of the blowing/suction. The small- and large-scale structures are separated with an adaptive scale-decomposition method, namely the empirical mode decomposition (EMD), which aims to analyse the scale-specific contribution of turbulent motions to friction-drag generation. Results unveil that blowing on the suction side of the airfoil is able to enhance the contribution of large-scale motions and to suppress that of small scales; however, suction behaves contrarily. The contributions related to cross-scale interactions remain almost unchanged with different control strategies.

In a shallow channel, the flow transfers most of its momentum vertically. Based on this observation, one often neglects the momentum that is transferred across the stream – the core assumption of the shallow-water theory. In the context of viscous flows, this approximation is referred to as the ‘lubrication theory’, in which one assumes that the shear stress exerted by the fluid on the substrate over which it flows is proportional to its velocity. Here, we revise this theory to account for the momentum that viscosity transfers across a shallow laminar flow, while keeping the problem low-dimensional. We then test the revised lubrication theory against analytical and numerical solutions of the exact problem. We find that, at a low computational cost, the present theory represents the actual flow more accurately than the classical lubrication approximation. This theoretical improvement, devised with laboratory rivers in mind, should also apply to other geophysical contexts, such as ice flows or forming lava domes.

A detailed analysis of steady coating flow of a thin film of a viscous fluid on the outside of a uniformly rotating horizontal circular cylinder in the absence of surface-tension effects but in the presence of a non-uniform pressure distribution due to an irrotational airflow with circulation shows that the presence of the airflow can result in qualitatively different behaviour of the fluid film from that in classical coating flow. Full-film solutions corresponding to a continuous film of fluid covering the entire cylinder are possible only when the flux and mass of fluid do not exceed critical values, which are determined in terms of the non-dimensional parameters $F$ and $K$ representing the speed of the far-field airflow and the circulation of the airflow, respectively. The qualitative changes in the behaviour of the film thickness as $F$ and $K$ are varied are described. In particular, the film thickness can have as many as four stationary points and, in general, has neither top-to-bottom nor right-to-left symmetry. In addition, when the circulation of the airflow is in the same direction as the rotation of the cylinder the maximum mass of fluid that can be supported on the cylinder is always less than that in classical coating flow, whereas when the circulation is in the opposite direction the maximum mass of fluid can be greater than that in classical coating flow.

A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for this purpose. Here, we consider a two-dimensional microstructure comprising an array of obstacles of smooth but arbitrary shape, the size and spacing of which can vary along the length of the porous medium. We use homogenisation via the method of multiple scales to systematically upscale a novel problem involving cells of varying area to obtain effective continuum equations for macroscale flow and transport. The equations are characterised by the local porosity, a local anisotropic flow permeability, an effective local anisotropic solute diffusivity and an effective local adsorption rate. These macroscale properties depend non-trivially on the two degrees of microstructural geometric freedom in our problem: obstacle size and obstacle spacing. We exploit this dependence to construct and compare scenarios where the same porosity profile results from different combinations of obstacle size and spacing. We focus on a simple example geometry comprising circular obstacles on a rectangular lattice, for which we numerically determine the macroscale permeability and effective diffusivity. We investigate scenarios where the porosity is spatially uniform but the permeability and diffusivity are not. Our results may be useful in the design of filters or for studying the impact of deformation on transport in soft porous media.

Fish typically swim by periodic bending of their bodies. Bending seems to follow a universal rule; it occurs at about one-third from the posterior end of the fish body with a maximum bending angle of about $30^{\circ }$. However, the hydrodynamic mechanisms that shaped this convergent design and its potential benefit to fish in terms of swimming speed and efficiency are not well understood. It is also unclear to what extent this bending is active or follows passively from the interaction of a flexible posterior with the fluid environment. Here, we use a self-propelled two-link model, with fluid–structure interactions described in the context of the vortex sheet method, to analyse the effects of both active and passive body bending on the swimming performance. We find that passive bending is more efficient but could reduce swimming speed compared with rigid flapping, but the addition of active bending could enhance both speed and efficiency. Importantly, we find that the phase difference between the posterior and anterior sections of the body is an important kinematic factor that influences performance, and that active antiphase flexion, consistent with the passive flexion phase, can simultaneously enhance speed and efficiency in a region of the design space that overlaps with biological observations. Our results are consistent with the hypothesis that fish that actively bend their bodies in a fashion that exploits passive hydrodynamics can at once improve speed and efficiency.

A canonical co-axial round-jet two-fluid atomizer where atomization occurs over a wide range of momentum ratios: $M=1.9 - 376.4$ is studied. The near field of the spray, where the droplet formation process takes place, is characterized and linked to droplet dispersion in the far field of the jet. Counterintuitively, our results indicate that in the low-momentum regime, increasing the momentum in the gas phase leads to less droplet dispersion. A critical momentum ratio of the order of $M_c=50$, that separates this regime from a high-momentum one with less dispersion, is found in both the near and far fields. A phenomenological model is proposed that determines the susceptibility of droplets to disperse beyond the nominal extent of the gas phase based on a critical Stokes number, $St=\tau _p/T_E=1.9$, formulated based on the local Eulerian large scale eddy turnover time, $T_E$, and the droplets’ response time, $\tau _p$. A two-dimensional phase space summarizes the extent of these different regimes in the context of spray characteristics found in the literature.

This paper presents an experimental investigation of aerofoil tones emitted by a controlled-diffusion aerofoil at low Mach number ($0.05$), moderate Reynolds number based on the chord length ($1.4 \times 10^{5}$) and moderate incidence ($5^{\circ }$ angle of attack). Wall-pressure measurements have been performed along the suction side of the aerofoil to reveal the acoustic source mechanisms. In particular, a feedback loop is found to extend from the aerofoil trailing edge to the regions near the leading edge where the flow encounters a mean favourable pressure gradient, and consists of acoustic disturbances travelling upstream. Simultaneous wall-pressure, velocity and far-field acoustic measurements have been performed to identify the boundary-layer instability responsible for tonal noise generation. Causality correlation between far-field acoustic pressure and wall-normal velocity fluctuations has been performed, which reveals the presence of a Kelvin–Helmholtz-type modal shape within the velocity disturbance field. Tomographic particle image velocimetry measurements have been performed to understand the three-dimensional aspects of this flow instability. These measurements confirm the presence of large two-dimensional rollers that undergo three-dimensional breakdown just upstream of the trailing edge. Finally, modal decomposition of the flow has been carried out using proper orthogonal decomposition, which demonstrates that the normal modes are responsible for aerofoil tonal noise. The higher normal modes are found to undergo regular modulations in the spanwise direction. Based on the observed modal shape, an explanation of aerofoil tonal noise amplitude reduction is given, which has been previously reported in modular or serrated trailing-edge aerofoils.

We present a numerical study on how tidal force and topography influence flow dynamics, transport and mixing in horizontal convection. Our results show that local energy dissipation near topography will be enhanced when the tide is sufficiently strong. Such enhancement is related to the height of the topography and increases as the tidal frequency $\omega$ decreases. The global dissipation is found to be less sensitive to the changes in $\omega$ when the latter becomes small and asymptotically approaches a constant value. We interpret the behaviour of the dissipation as a result of the competition among the dominant forces in the system. According to which mechanism prevails, the flow state of the system can be divided into three regimes, which are the buoyancy-, tide- and drag-control regimes. We show that the mixing efficiency $\eta$ for different tidal energy and topography height can be well described by a universal function $\eta \approx \eta _{HC}/(1+\mathcal {R})$, where $\eta _{HC}$ is the mixing efficiency in the absence of tide and $\mathcal {R}$ is the ratio between tidal and available potential energy inputs. With this, one can also determine the dominant mechanism at a certain ocean region. We further derive a power law relationship connecting the mixing coefficient and the tidal Reynolds number.