This numerical study presents a simple but extremely effective way to considerably enhance heat transport in turbulent wall-bounded multiphase flows, namely by using oleophilic walls. As a model system, we pick the Rayleigh–Bénard set-up, filled with an oil–water mixture. For oleophilic walls, using only $10\,\%$ volume fraction of oil in water, we observe a remarkable heat transport enhancement of more than $100\,\%$ as compared to the pure water case. In contrast, for oleophobic walls, the enhancement is only of about $20\,\%$ as compared to pure water. The physical explanation of the heat transport increment for oleophilic walls is that thermal plumes detach from the oil-rich boundary layer and carry the heat with them. In the bulk, the oil–water interface prevents the plumes from mixing with the turbulent water bulk and to diffuse their heat. To confirm this physical picture, we show that the minimum amount of oil necessary to achieve the maximum heat transport is set by the volume fraction of the thermal plumes. Our findings provide guidelines of how to optimize heat transport in wall-bounded thermal turbulence. Moreover, the physical insight of how coherent structures are coupled with one of the phases of a two-phase system has very general applicability for controlling transport properties in other turbulent wall-bounded multiphase flows.

Fluid entering the periphery of a steadily rotating cylindrical tank exits through an off-axis drain hole, located in the tank's base at the half-radius. Experiments show that, though a concentrated vortex forms over the drain, it soon advects around the tank in what is at first a circular path. Though inviscid vortex dynamics predicts continued motion, our experiments show that the vortex moves inwards from the predicted circular path, finally coming to rest at approximately $50^{\circ }$ from the drain. In this final state, the vorticity is concentrated in a thin shear layer bounding an irrotational core, which passes over the drain. The broadening of the vortex structure and eventual steady-state formation are believed to be due to the growing boundary layer on the outer wall.

The instability and dynamics of a vertical oscillatory boundary layer in a container filled with a stratified fluid are addressed. Past experiments have shown that when the boundary oscillation frequency is of the same order as the buoyancy frequency, the system is unstable to a herringbone pattern of oblique waves. Prior studies assuming the basic state to be a unidirectional oscillatory shear flow were unable to account for the oblique waves. By accounting for confinement effects present in the experiments, and the ensuing three-dimensional structure of the basic state, we are able to numerically reproduce the experimental observations, opening the door to fully analysing the impacts of stratification on such boundary layers.

The central open question about Rayleigh–Bénard convection – buoyancy-driven flow in a fluid layer heated from below and cooled from above – is how vertical heat flux depends on the imposed temperature gradient in the strongly nonlinear regime where the flows are typically turbulent. The quantitative challenge is to determine how the Nusselt number $Nu$ depends on the Rayleigh number $Ra$ in the $Ra\to \infty$ limit for fluids of fixed finite Prandtl number $Pr$ in fixed spatial domains. Laboratory experiments, numerical simulations and analysis of Rayleigh's mathematical model have yet to rule out either of the proposed ‘classical’ $Nu \sim Ra^{1/3}$ or ‘ultimate’ $Nu \sim Ra^{1/2}$ asymptotic scaling theories. Among the many solutions of the equations of motion at high $Ra$ are steady convection rolls that are dynamically unstable but share features of the turbulent attractor. We have computed these steady solutions for $Ra$ up to $10^{14}$ with $Pr=1$ and various horizontal periods. By choosing the horizontal period of these rolls at each $Ra$ to maximize $Nu$, we find that steady convection rolls achieve classical asymptotic scaling. Moreover, they transport more heat than turbulent convection in experiments or simulations at comparable parameters. If heat transport in turbulent convection continues to be dominated by heat transport in steady rolls as $Ra\to \infty$, it cannot achieve the ultimate scaling.

We propose a scientifically rigorous framework to find realistic optimal geometries of wave energy converters (WECs). For specificity, we assume WECs to be axisymmetric point absorbers in a monochromatic unidirectional incident wave, all within the context of linearised potential theory. We consider separately the problem of a WEC moving and extracting wave energy in heave only and then the more general case of motion and extraction in combined heave, surge and pitch. We describe the axisymmetric geometries using polynomial basis functions, allowing for discontinuities in slope. Our framework involves ensuring maximum power, specifying practical motion constraints and then minimising surface area (as a proxy for cost). The framework is robust and well-posed, and the optimisation produces feasible WEC geometries. Using the proposed framework, we develop a systematic computational and theoretical approach, and we obtain results and insights for the optimal WEC geometries. The optimisation process is sped up significantly by a new theoretical result to obtain roots of the heave resonance equation. For both the heave-only, and the heave-surge-pitch combined problems, we find that geometries which protrude outward below the waterline are generally optimal. These optimal geometries have up to 73 % less surface area and 90 % less volume than the optimal cylinders which extract the same power.

Motivated by the need for compact descriptions of the evolution of non-classical wakes behind yawed wind turbines, we develop an analytical model to predict the shape of curled wakes. Interest in such modelling arises due to the potential of wake steering as a strategy for mitigating power reduction and unsteady loading of downstream turbines in wind farms. We first estimate the distribution of the shed vorticity at the wake edge due to both yaw offset and rotating blades. By considering the wake edge as an ideally thin vortex sheet, we describe its evolution in time moving with the flow. Vortex sheet equations are solved using a power series expansion method, and an approximate solution for the wake shape is obtained. The vortex sheet time evolution is then mapped into a spatial evolution by using a convection velocity. Apart from the wake shape, the lateral deflection of the wake including ground effects is modelled. Our results show that there exists a universal solution for the shape of curled wakes if suitable dimensionless variables are employed. For the case of turbulent boundary layer inflow, the decay of vortex sheet circulation due to turbulent diffusion is included. Finally, we modify the Gaussian wake model by incorporating the predicted shape and deflection of the curled wake, so that we can calculate the wake profiles behind yawed turbines. Model predictions are validated against large-eddy simulations and laboratory experiments for turbines with various operating conditions.

The aim of this study is to investigate experimentally the transition from a rigid regime to a deformed regime for flexible discs freely advected in turbulent flows. For a given disc, the amplitude of the deformation is expected to increase when its bending modulus decreases or when the turbulent kinetic energy increases. To quantify this qualitative argument, experiments are performed where the deformation of flexible discs is measured using three cameras. The amplitude of the deformation has been characterised by the eigenvalues of the moment of inertia tensor. Experimental results exhibit a transition from a rigid regime to a deformed regime that depends on the size, the density and the flexibility of the disc and the turbulent kinetic energy. The modelling of this transition is a generalisation and an extension of the previous models used to characterise the deformation of flexible fibres in turbulent flows.

The stability of the Taylor vortex flow in Newtonian and shear-thinning fluids is investigated in the case of a wide gap Taylor–Couette system. The considered radius ratio is $\eta = R_1/R_2=0.4$. The aspect ratio (length over the gap width) of experimental configuration is 32. Flow visualization and measurements of two-dimensional flow fields with particle image velocimetry are performed in a glycerol aqueous solution (Newtonian fluid) and in xanthan gum aqueous solutions (shear-thinning fluids). The experiments are accompanied by axisymmetric numerical simulations of Taylor–Couette flow in the same gap of a Newtonian and a purely viscous shear-thinning fluid described by the Carreau model. The experimentally observed critical Reynolds and wavenumbers at the onset of Taylor vortices are in very good agreement with that obtained from a linear theory assuming a purely viscous shear-thinning fluid and infinitely long cylinders. They are not affected by the viscoelasticity of the used fluids. For the Newtonian fluid, the Taylor vortex flow (TVF) regime is found to bifurcate into a wavy vortex flow with a high frequency and low amplitude of axial oscillations of the vortices at ${Re} = 5.28 \, {Re}_c$. At ${Re} = 6.9 \, {Re}_c$, the frequency of oscillations decreases and the amplitude increases abruptly. For the shear-thinning fluids the secondary instability conserves axisymmetry. The latter is characterized by an instability of the array of vortices leading to a continuous sequence of creation and merging of vortex pairs. Axisymmetric numerical simulations reproduce qualitatively very well the experimentally observed flow behaviour.

We demonstrate that in plane Couette turbulence a separation of the velocity field in large and small scales according to a streamwise Fourier decomposition allows us to identify an active subspace comprising a small number of the gravest streamwise components of the flow that can synchronize all the remaining streamwise flow components. The critical streamwise wavelength, $\ell _{x c}$, that separates the active from the synchronized passive subspace is identified as the streamwise wavelength at which perturbations to the time-dependent turbulent flow with streamwise wavelengths $\ell _x<\ell _{xc}$ have negative characteristic Lyapunov exponents. The critical wavelength is found to be approximately 130 wall units and obeys viscous scaling at these Reynolds numbers.

In collisional gas–solid flows, dense particle clusters are often observed that greatly affect the transport properties of the mixture. The characterisation and prediction of this phenomenon are challenging due to limited optical access, the wide range of scales involved and the interplay of different mechanisms. Here, we consider a laboratory setup in which particles fall against upward-moving air in a square vertical duct: a classic configuration in riser reactors. The use of non-cohesive, monodispersed, spherical particles and the ability to independently vary the solid volume fraction ($\varPhi _V = 0.1\,\% - 0.8\,\%$) and the bulk airflow Reynolds number ($Re_{bulk} = 300 - 1200$) allows us to isolate key elements of the multiphase dynamics, providing the first laboratory observation of cluster-induced turbulence. Above a threshold $\varPhi _V$, the system exhibits intense fluctuations of concentration and velocity, as measured by high-speed imaging via a backlighting technique which returns optically depth-averaged fields. The space–time autocorrelations reveal dense and persistent mesoscale structures falling faster than the surrounding particles and trailing long wakes. These are shown to be the statistical footprints of visually observed clusters, mostly found in the vicinity of the walls. They are identified via a percolation analysis, tracked in time, and characterised in terms of size, shape, location and velocity. Larger clusters are denser, longer-lived and have greater descent velocity. At the present particle Stokes number, the threshold $\varPhi _V \sim 0.5$ % (largely independent from $Re_{bulk}$) is consistent with the view that clusters appear when the typical interval between successive collisions is shorter than the particle response time.

This paper presents results of three-dimensional direct numerical simulations (DNS) and global linear stability analyses of a viscous incompressible flow past a finite-length cylinder with two free flat ends. The cylindrical axis is normal to the streamwise direction. The work focuses on the effects of aspect ratios (in the range of $0.5\leq {\small \text{AR}} \leq 2$, cylinder length over diameter) and Reynolds numbers ($Re\leq 1000$ based on cylinder diameter and uniform incoming velocity) on the onset of vortex shedding in this flow. All important flow patterns have been identified and studied, especially as ${\small \text{AR}}$ changes. The appearance of a steady wake pattern when ${\small \text{AR}} \leq 1.75$ has not been discussed earlier in the literature for this flow. Linear stability analyses based on the time-mean flow has been applied to understand the Hopf bifurcation past which vortex shedding happens. The nonlinear DNS results indicate that there are two vortex shedding patterns at different $Re$, one is transient and the other is nonlinearly saturated. The vortex-shedding frequencies of these two flow patterns correspond to the eigenfrequencies of the two global modes in the stability analysis of the time-mean flow. Wherever possible, we compare the results of our analyses to those of the flows past other short-${\small \text{AR}}$ bluff bodies in order that our discussions bear more general meanings.

The logarithmic dependence of streamwise turbulence intensity has been observed repeatedly in recent experimental and direct numerical simulation data. However, its spectral counterpart, a well-developed $k^{-1}$ spectrum ($k$ is the spatial wavenumber in a wall-parallel direction), has not been convincingly observed from the same data. In the present study, we revisit the spectrum-based attached eddy model of Perry and co-workers, who proposed the emergence of a $k^{-1}$ spectrum in the inviscid limit, for small but finite $z/\delta$ and for finite Reynolds numbers ($z$ is the wall-normal coordinate, and $\delta$ is the outer length scale). In the upper logarithmic layer (or inertial sublayer), a reexamination reveals that the intensity of the spectrum must vary with the wall-normal location at order of $z/\delta$, consistent with the early observation argued with ‘incomplete similarity’. The streamwise turbulence intensity is subsequently calculated, demonstrating that the existence of a well-developed $k^{-1}$ spectrum is not a necessary condition for the approximate logarithmic wall-normal dependence of turbulence intensity – a more general condition is the existence of a premultiplied power-spectral intensity of $O(1)$ for $O(1/\delta ) < k < O(1/z)$. Furthermore, it is shown that the Townsend–Perry constant must be weakly dependent on the Reynolds number. Finally, the analysis is semi-empirically extended to the lower logarithmic layer (or mesolayer), and a near-wall correction for the turbulence intensity is subsequently proposed. All the predictions of the proposed model and the related analyses/assumptions are validated with high-fidelity experimental data (Samie et al., J. Fluid Mech., vol. 851, 2018, pp. 391–415).

An experimental study is performed to investigate the effects of the extensional rheological properties of drag-reducing wormlike micellar solutions on the vortex deformation and turbulence statistics in two-dimensional (2-D) turbulent flow. A self-standing 2-D turbulent flow was used as the experimental set-up, and the flow was observed through interference pattern monitoring and particle image velocimetry. Vortex shedding and turbulence statistics in the flow were affected by the formation of wormlike micelles and were enhanced by increasing the molar ratio of the counter-ion supplier to the surfactant, ξ, or by applying extensional stresses to the solution. In the 2-D turbulent flow, extensional and shear rates were applied to the fluids around a comb of equally spaced cylinders. This induced the formation of a structure made of wormlike micelles just behind the cylinder. The flow-induced structure influenced the velocity fields around the comb and the turbulence statistics. A characteristic increase in turbulent energy was observed, which decreased slowly downstream. The results implied that the characteristic modification of the 2-D turbulent flow of the drag-reducing surfactant solution was affected by the formation and slow relaxation of the flow-induced structure. The relaxation process of the flow-induced structure made of wormlike micelles was very different from that of the polymers.

Shock-induced light-fluid-layer evolution is firstly investigated experimentally and theoretically. Specifically, three quasi-one-dimensional helium gas layers with different layer thicknesses are generated to study the wave patterns and interface motions. Six quasi-two-dimensional helium gas layers with diverse layer thicknesses and amplitude combinations are created to explore the Richtmyer–Meshkov instability of a light-fluid layer. Due to the multiple reflected shocks reverberating inside a light-fluid layer, the speeds of the two interfaces gradually converge, and the layer thickness saturates eventually. A general one-dimensional theory is adopted to describe the two interfaces’ motions and the layer thickness variations. It is found that, for the first interface, the end time of its phase reversal determines the influence of the reflected shocks on it. However, the reverberated shocks indeed lead to the second interface being more unstable. When the two interfaces are initially in phase, and the initial fluid layer is very thin, the two interfaces’ spike heads collide and stabilise the two interfaces. Linear and nonlinear models are successfully adopted by considering the interface-coupling effect and the reverberated shocks to predict the two interfaces’ perturbation growths in all regimes. The interfacial instability of a light-fluid layer is quantitatively compared with that of a heavy-fluid layer. It is concluded that the kind of waves reverberating inside a fluid layer significantly affects the fluid-layer evolution.

We study forced, rapidly rotating and stably stratified turbulence in an elongated domain using an asymptotic expansion at simultaneously low Rossby number $\mathit {Ro}\ll 1$ and large domain height compared with the energy injection scale, $h=H/\ell _{in}\gg 1$. The resulting equations depend on the parameter $\lambda =(h \mathit {Ro} )^{-1}$ and the Froude number $\mathit {Fr}$. An extensive set of direct numerical simulations (DNS) is performed to explore the parameter space $(\lambda,\mathit {Fr})$. We show that a forward energy cascade occurs in one region of this space, and a split energy cascade outside it. At weak stratification (large $\mathit {Fr}$), an inverse cascade is observed for sufficiently large $\lambda$. At strong stratification (small $\mathit {Fr}$) the flow becomes approximately hydrostatic and an inverse cascade is always observed. For both weak and strong stratification, we present theoretical arguments supporting the observed energy cascade phenomenology. Our results shed light on an asymptotic region in the phase diagram of rotating and stratified turbulence, which is difficult to attain by brute-force DNS.

The flow around and behind a sphere in a linear density gradient has served as a model problem for both body-generated wakes in atmospheres and oceans, and as a means of generating a patch of turbulence that then decays in a stratified ambient. Here, experiments and numerical simulations are conducted for 20 values of Reynolds number, $Re$, and internal Froude number, $Fr$, where each is varied independently. In all cases, the early wake is affected by the background density gradient, notably in the form of the body-generated lee waves. Mean and fluctuating quantities do not reach similar states, and their subsequent evolution would not be collapsible under any universal scaling. There are five distinguishable flow regimes, which mostly overlap with previous literature based on qualitative visualisations and, in this parameter space, they maintain their distinguishing features up to and including buoyancy times of 20. The possible relation of the low $\{Re, Fr\}$ flows to their higher $\{Re, Fr\}$ counterparts is discussed.

Thrust and/or efficiency of a pitching foil (mimicking a tail of swimming fish) can be enhanced by tweaking the pitching waveform. The literature, however, show that non-sinusoidal pitching waveforms can enhance either thrust or efficiency but not both simultaneously. With the knowledge and inspiration from nature, we devised and implemented a novel asymmetrical sinusoidal pitching motion that is a combination of two sinusoidal motions having periods T1 and T2 for the forward and retract strokes, respectively. The motion is represented by period ratio $\mathrm{\mathbb{T}} = {T_1}/T$, where T = (T1 + T2)/2, with $\mathrm{\mathbb{T}} > 1.00$ giving the forward strokes (from equilibrium to extreme position) slower than the retract strokes (from extreme to equilibrium position) and vice versa. The novel pitching motion enhances both thrust and efficiency for $\mathrm{\mathbb{T}} > 1.00$. The enhancement results from the resonance between the shear-layer roll up and the increased speed of the foil. Four swimming regimes, namely normal swimming, undesirable, floating and ideal are discussed, based on instantaneous thrust and power. The results from the novel pitching motion display similarities with those from fish locomotion (e.g. fast start, steady swimming and braking). The $\mathrm{\mathbb{T}} > 1.00$ motion in the faster stroke has the same characteristics and results as the fast start of prey to escape from a predator while $\mathrm{\mathbb{T}} < 1.00$ imitates braking locomotion. While $\mathrm{\mathbb{T}} < 1.00$ enhances the wake deflection at high amplitude-based Strouhal numbers (StA = fA/U∞, where f and A are the frequency and peak-to-peak amplitude of the pitching, respectively, and U∞ is the freestream velocity), $\mathrm{\mathbb{T}} > 1.00$ improves the wake symmetry, suppressing the wake deflection. The wake characteristics including wake width, jet velocity and vortex structures are presented and connected with $S{t_d}( = fd/{U_\infty })$, ${A^{\ast}}( = A/d)$ and $\mathrm{\mathbb{T}}$, where d is the maximum thickness of the foil.

The shear instability occurring at the interface between a slow water layer and a fast air stream is a complex phenomenon driven by momentum and viscosity differences across the interface, velocity gradients as well as by injector geometries. Simulating such an instability under experimental conditions is numerically challenging and few studies exist in the literature. This work aims at filling a part of this gap by presenting a study of the convergence between two-dimensional simulations, linear theory and experiments, in regimes where the instability is triggered by the confinement, i.e. finite thicknesses of gas and liquid streams. It is found that very good agreement between the three approaches is obtained. Moreover, using simulations and linear theory, we explore in detail the effects of confinement on the stability of the flow and on the transition between absolute and convective instability regimes, which is shown to depend on the length scale of the confinement as well as on the dynamic pressure ratio. In the absolute regime under study, the interfacial wave frequency is found to be inversely proportional to the smallest injector size (liquid or gas).

This paper investigates the air flow induced by a rigid circular disk or piston vibrating harmonically along its axis of symmetry in the immediate vicinity of a parallel surface. Previous attempts to characterize these so-called ‘squeeze-film’ systems largely relied on simplifications afforded by neglecting either fluid acceleration or viscous forces inside the thin enclosed gas layer. The present viscoacoustic analysis employs the asymptotic limit of small vibration amplitudes to investigate the flow by systematic reduction of the Navier–Stokes equations in two distinct flow regions, namely, the inner gaseous film where streamlines are nearly parallel to the confining walls and the near-edge region of non-slender flow that features gas exchange with the surrounding stagnant atmosphere. The flow in the gaseous film depends on the relevant Stokes number, defined as the ratio of the characteristic viscous time across the film to the characteristic oscillation time, and on a compressibility parameter, defined as the square of the ratio of the acoustic time for radial pressure equilibration to the oscillation time. A Strouhal number based on the local residence time emerges as an additional governing parameter for the near-edge region, which is incompressible at leading order. The method of matched asymptotic expansions is used to describe the solution in both regions, across which the time-averaged pressure exhibits comparable variations that give opposing contributions to the resulting time-averaged force experienced by the disk or piston. A diagram structured with the Stokes number and compressibility parameter as coordinates reveals that this steady squeeze-film force, typically repulsive for small values of the Stokes number, alternates to attraction across a critical separation contour in the parametric domain that exists for all Strouhal numbers. This analysis provides, for the first time, a unifying viscoacoustic theory of axisymmetric squeeze films, which yields a reduced parametric description for the time-averaged repulsion/attraction force that is potentially useful in applications including non-contact fluid bearings and robot locomotion.

A recently developed mixing length model of the turbulent shear stress in pipe flow is used to solve the streamwise momentum equation for fully developed channel flow. The solution for the velocity profile takes the form of an integral that is uniformly valid from the wall to the channel centreline at all Reynolds numbers from zero to infinity. The universal velocity profile accurately approximates channel flow direct numerical simulation (DNS) data taken from several sources. The universal velocity profile also provides a remarkably accurate fit to simulated and experimental flat plate turbulent boundary layer data including zero and adverse pressure gradient data. The mixing length model has five free parameters that are selected through an optimization process to provide an accurate fit to data in the range $R_\tau = 550$ to $R_\tau = 17\,207$. Because the velocity profile is directly related to the Reynolds shear stress, certain statistical properties of the flow can be studied such as turbulent kinetic energy production. The examples presented here include numerically simulated channel flow data from $R_\tau = 550$ to $R_\tau =8016$, zero pressure gradient (ZPG) boundary layer simulations from $R_\tau =1343$ to $R_\tau = 2571$, zero pressure gradient turbulent boundary layer experimental data between $R_\tau = 2109$ and $R_\tau = 17\,207$, and adverse pressure gradient boundary layer data in the range $R_\tau = 912$ to $R_\tau = 3587$. An important finding is that the model parameters that characterize the near-wall flow do not depend on the pressure gradient. It is suggested that the new velocity profile provides a useful replacement for the classical wall-wake formulation.