Large-eddy simulation of a particle-laden flow over an erodible bed is performed to investigate the effect of heavy, saltating particles on turbulence modulation, using the Eulerian–Lagrangian point-particle approach with two-way coupling. The flow into which the solid particles are introduced is a turbulent open channel flow with particle-free friction Reynolds numbers of 3730 and 4200. The inter-particle collisions are not considered, whereas the particle-bed collisions are described by splashing models. Simulation results show that the addition of particles reduces the mean streamwise fluid velocity. The streamwise fluctuating velocity and Reynolds stress are damped while the vertical and spanwise turbulence intensities are enhanced in the near-bed region. The turbulence intensities and Reynolds stress in the outer layer are apparently increased. These effects become more pronounced as the Reynolds number increases. Correlation scales of the turbulence structures increase in the near-bed region and decrease in the outer region. The modulation mechanism of turbulence is revealed. That is, the range and degree of turbulence enhancement by ascending particles in the near-bed region are much larger than those of turbulence attenuation by descending particles, which results in the redistribution of turbulent kinetic energy from the streamwise to the spanwise and vertical directions. This effect extends to the outer region via saltating particles by forming ‘active’ roughness elements. The premultiplied energy spectra of the streamwise velocity show that the enhancement of outer turbulent kinetic energy by saltating particles occurs in a wide range of wavelengths from the intermediate to very large scale.

The experimental data for the mean velocity are analysed in the inner layer for a turbulent boundary layer at significant adverse pressure gradient and Reynolds numbers up to $\textit {Re}_\theta =57\,000$. The aim is to determine the resilience of the log law for the mean velocity, the possible change of the von Kármán constant $\kappa$ and the appearance of a square-root law above the log law at significant adverse pressure gradients. In the wind-tunnel experiment, the adverse pressure gradient is imposed by an $S$-shaped deflection of the contour model which is mounted on a wind-tunnel sidewall. A large-scale particle imaging velocimetry method is applied to measure the streamwise evolution of the flow over a streamwise distance of 15 boundary layer thicknesses. In the adverse pressure gradient region, microscopic and three-dimensional Lagrangian particle tracking velocimetry are used to measure the mean velocity and the Reynolds stresses down to the viscous sublayer. Oil-film interferometry is used to determine the wall shear stress. The log law in the mean-velocity profile is found to be a robust feature at adverse pressure gradient, but its region is thinner than its zero pressure gradient counterpart, and its slope is altered. A square-root law emerges above the log law, extending to the wall distance the log law typically occupies at zero pressure gradient. Lower values for $\kappa$ are found than for zero pressure gradient turbulent boundary layers, but the reduction is within the uncertainty of the measurement.

Simultaneous wall-pressure and high-speed particle image velocimetry measurements were used to identify the coherent structures that generate low- and mid-frequency wall-pressure fluctuations in a turbulent boundary layer at a friction Reynolds number of $Re_\tau =2600$. The coherence function between wall pressure and velocity at a range of wall-normal locations revealed two distinct frequency bands of high coherence that span the low- and mid-frequency regions of the wall-pressure spectrum. Pressure was filtered to isolate the frequencies associated with each region of high coherence, and space–time pressure-velocity correlations were computed using the filtered signals to expose the motions responsible for the observed pressure-velocity coupling. The resulting correlation patterns were attributed to very-large-scale motions (VLSMs) and hairpin packets, revealing that these two types of coherent motions are the dominant sources of wall-pressure fluctuations at the low and mid frequencies. Although the VLSMs and hairpin packets are closely related, the mechanisms by which these motions affect wall pressure were found to be different. The VLSMs were found to cause positive and negative wall-pressure fluctuations via splatting and lifting of fluid at the wall, respectively. In contrast, hairpin packets affected wall pressure because of their low-pressure vortex cores and regions of high-pressure stagnation. The frequency at which the wall-pressure source changes from the VLSMs to the hairpin packets coincided with the peak of the wall-pressure spectrum, suggesting that the peak may be a result of the transition between pressure sources that occurs at the same point in the frequency domain.

Through ensemble-based data assimilation, we address one of the most notorious difficulties in phase-resolved ocean wave forecast, regarding the deviation of numerical solution from the true surface elevation due to the chaotic nature of and underrepresented physics in the nonlinear wave models. In particular, we develop a coupled approach of the high-order spectral (HOS) method with the ensemble Kalman filter (EnKF), through which the measurement data can be incorporated into the simulation to improve the forecast performance. A unique feature in this coupling is the mismatch between the predictable zone and measurement region, which is accounted for through a special algorithm to modify the analysis equation in EnKF. We test the performance of the new EnKF–HOS method using both synthetic data and real radar measurements. For both cases (though differing in details), it is shown that the new method achieves much higher accuracy than the HOS-only method, and can retain the phase information of an irregular wave field for an arbitrarily long forecast time with sequentially assimilated data.

Flowing granular materials segregate due to differences in particle size (driven by percolation) and density (driven by buoyancy). Modelling the segregation of mixtures of large/heavy particles and small/light particles is challenging due to the opposing effects of the two segregation mechanisms. Using discrete element method (DEM) simulations of combined size and density segregation we show that the segregation velocity is well described by a model that depends linearly on the local shear rate and quadratically on the species concentration for free surface flows. Concentration profiles predicted by incorporating this segregation velocity model into a continuum advection–diffusion–segregation transport model match DEM simulation results well for a wide range of particle size and density ratios. Most surprisingly, the DEM simulations and the segregation velocity model both show that the segregation direction for a range of size and density ratios depends on the local species concentration. This leads to a methodology to determine the combination of particle size ratio, density ratio and particle concentration for which a bidisperse mixture will not segregate.

This study presents an innovative approach towards the generation and decay of turbulence in the Taylor–Couette system. The outer cylinder was brought to an abrupt stoppage that generated turbulence in the system, which was initially in the laminar flow regime. Two complementary experimental approaches, namely visualizations and stereo-particle image velocimetry (PIV) measurements, were used to better understand the presented phenomenon for only external cylinder rotation. A moving time average technique was developed due to the continuous change in the length scales throughout the generation and decay process. The different stages of the generation and decay of turbulence were described and characterized through dynamic quantities such as the kinetic energy. This new approach towards the generation and decay of turbulence in the Taylor–Couette flow should help significantly in future endeavours.

We investigate the dynamics of inertial particles in homogeneous isotropic turbulence, under one-way momentum coupling, using a new computational approach that incorporates the effect of long-range many-body aerodynamic interactions along with the short-range lubrication forces. The implementation couples hybrid direct numerical simulations (HDNS) with the analytical solutions of two rigid spheres moving in an unbounded fluid. Concerning the velocity field seen by the particles, the algorithm switches from the flow solution in terms of HDNS to analytical formulae when the separation distance between particles becomes comparable to their average radius. Standard HDNS is unable to correctly represent the short-range interactions since this method is based on the superposition of the Stokes solutions for single spheres. Our results show that for the turbulent kinetic energy dissipation rates typical of atmospheric clouds, the radial relative velocities (RRVs) of the droplets increase, and the radial distribution function (RDF) decreases in the near-contact region if the lubrication forces are taken into account. These changes are more pronounced when the effect of gravity is considered. Away from the contact region, there is not much change in RRVs and RDFs. For turbulent clouds with lower dissipation rates lubrication forces significantly enhance the average RRV in the limit of low Stokes number. This enhancement, however, is statistically insignificant because the number of particle pairs at close proximity is very small. The effect of mass loading on the collision statistics is also investigated, demonstrating an increase in RRV and a reduction in RDF with the droplet concentration.

We report on an investigation of bubble-induced turbulence. Bubbles of a size larger than the dissipative scale cannot be treated as pointwise inclusions, and generate important hydrodynamic fields in the carrier fluid when in motion. Furthermore, bubble motions may induce a collective agitation due to hydrodynamic interactions which display some turbulent-like features. We tackle this complex phenomenon numerically, performing direct numerical simulations with a volume-of-fluid method. In the first part of the work, we perform both two-dimensional and three-dimensional tests in order to determine appropriate numerical and physical parameters. We then carry out a highly resolved simulation of a three-dimensional bubble column, with a set-up and physical parameters similar to those used in laboratory experiments. This is the largest simulation attempted for such a configuration and is only possible thanks to adaptive grid refinement. Results are compared both with experiments and previous coarse-mesh numerical simulations. In particular, the one-point probability density function of the velocity fluctuations is in good agreement with experiments. The spectra of the kinetic energy show a clear $k^{-3}$ scaling. The mechanisms underlying the energy transfer and notably the possible presence of a cascade are unveiled by a local scale-by-scale analysis in physical space. The comparison with previous simulations indicates to what extent simulations not fully resolved may yet give correct results, from a statistical point of view.

We present an experimental study of a turbulent boundary layer (TBL) control on a flat plate using plasma actuators. Three different configurations of the actuators produce spanwise arrays of large-scale streamwise vortices (LSSVs). An ultra-high-resolution floating element (FE) force balance, developed in house and calibrated using μ-particle tracking velocimetry, is employed to measure wall friction. The FE captures a drag reduction (DR) of up to 26 % on the FE area (667 × 1333 wall units), downstream of the actuators. The local DR persists downstream, well after the LSSVs disappear. Both plasma-generated flow and the TBL under control are compared with an uncontrolled TBL. The maximum DR takes place when the LSSVs producing wall jets reach a spanwise velocity of 3.9 in wall units. The flow is altered by up to 29 % of the TBL thickness, with a drop in the new vortices due to the control-induced stabilization of the wall streaks. The local friction is characterized by three distinct spatial regions of drag increase, pronounced DR and drag recovery – all connected to the LSSVs. The LSSVs push the streaks to the middle between two adjacent actuators, suppressing transient growth and near-wall turbulent production. A DR mechanism is proposed.

A Lagrangian experimental study of an axisymmetric turbulent water jet is performed to investigate the highly anisotropic and inhomogeneous flow field. Measurements are conducted within a Lagrangian exploration module, an icosahedron apparatus, to facilitate optical access of three cameras. Stereoscopic particle tracking velocimetry results in three-component tracks of position, velocity and acceleration of the tracer particles within the vertically oriented jet with a Taylor-based Reynolds number ${\textit {Re}}_\lambda \simeq 230$. Analysis is performed at seven locations from 15 diameters up to 45 diameters downstream. Eulerian analysis is first carried out to obtain critical parameters of the jet and relevant scales, namely the Kolmogorov and large (integral) scales as well as the energy dissipation rate. Lagrangian statistical analysis is then performed on velocity components stationarised following methods inspired by Batchelor (J. Fluid Mech., vol. 3, 1957, pp. 67–80), which aim to extend stationary Lagrangian theory of turbulent diffusion by Taylor to the case of self-similar flows. The evolution of typical Lagrangian scaling parameters as a function of the developing jet is explored and results show validation of the proposed stationarisation. The universal scaling constant $C_0$ (for the Lagrangian second-order structure function), as well as Eulerian and Lagrangian integral time scales, are discussed in this context. Constant $C_0$ is found to converge to a constant value (of the order of $C_0 = 3$) within 30 diameters downstream of the nozzle. Finally, the occurrence of finite particle size effects is investigated through consideration of acceleration-dependent quantities.

Internal wave generation is fundamentally the conversion of barotropic to baroclinic energy that often occurs due to vertical acceleration of stratified flows over topographic features. Acceleration results in a phase lag between density (pressure) perturbations and the barotropic velocity. To estimate the conversion of barotropic to baroclinic energy, the density perturbation is often calculated using a time-invariant background density. Other phenomena, however, can also alter the phasing of density perturbations and vertical velocities, such as barotropic tidal heaving and internal wave interactions. Consequently, accurately accounting for these dynamics in energy budgets is important. Tidal averaging or modal decomposition are often used to isolate topographic energy conversion in the presence of these other phenomena. However, while effective, these methods do not provide insights into the dynamics of conversion either through time or over depth. Here, we present a new analytical approach to calculating barotropic to baroclinic conversion using a time-varying background density. Our method results in an additional term in the baroclinic energy budget that directly accounts for barotropic tidal heaving and internal wave interactions, depending on the formulation of the background density. The tidally averaged, domain-integrated conversion rate is consistent across methods. Isolation of topographic conversion demonstrates that conversion due to interactions between internal wave beams and barotropic tidal heaving lead to relatively small differences in the overall conversion. However, using a time-varying background density allows for full decomposition of barotropic to baroclinic conversion through time and the identification of regions where negative conversion related to mixing actually occurs.

Darcy's law is used widely to model flow in heterogeneous porous media via a spatially varying conductivity field. The isotropic Darcy equation imposes significant constraints on the allowable Lagrangian kinematics of the flow field and thus upon scalar transport. These constraints stem from the fact that the helicity density in these flows is identically zero and so the flow does not admit closed or knotted flow paths. This implies that steady Darcy flow possesses a particularly simple flow topology which involves streamlines that do not possess closed orbits, knots or linked vortex lines. This flow structure is termed ‘complex lamellar’ and consists of fully integrable (in the dynamical systems sense) streamlines which admit two analytic constants of motion and so preclude chaotic advection. In this study we show that these constants of motion correspond to a pair of streamfunctions which are single valued and topologically planar, and the intersections of the level sets of these invariants correspond to streamlines of the flow. We show that the streamfunctions and iso-potential surfaces of the flow form a semi-orthogonal coordinate system, that naturally recovers the topological constraints imposed on the Lagrangian kinematics of these flows. We use this coordinate system to investigate the impact of these constraints upon the kinematics of Darcy flow, including the deformation of fluid elements and transverse macrodispersion of solutes in the absence of local dispersion. These results shed new light on the relevance and limitations of isotropic Darcy flow as a model of transport, mixing and reaction in porous media.

Using numerical simulations, we probe the fluid flow in an axisymmetric peristaltic vessel fitted with elastic bi-leaflet valves. In this biomimetic system that mimics the flow generated in lymphatic vessels, we investigate the effects of the valve and vessel properties on pumping performance of the valved peristaltic vessel. The results indicate that valves significantly increase pumping by reducing backflow. The presence of valves, however, increases the viscous resistance, therefore requiring greater work compared to valveless vessels. The benefit of the valves is the most significant when the fluid is pumped against an adverse pressure gradient and for low vessel contraction wave speeds. We identify the optimum vessel and valve parameters leading to the maximum pumping efficiency. We show that the optimum valve elasticity maximizes the pumping flow rate by allowing the valve to block the backflow more effectively while maintaining low resistance during the forward flow. We also examine the pumping in vessels where the vessel contraction amplitude is a function of the adverse pressure gradient, as found in lymphatic vessels. We find that, in this case, the flow is limited by the work generated by the contracting vessel, suggesting that the pumping in lymphatic vessels is constrained by the performance of the lymphatic muscle. Given the regional heterogeneity of valve morphology observed throughout the lymphatic vasculature, these results provide insight into how these variations might facilitate efficient lymphatic transport in the vessel's local physiologic context.

This paper presents the results of the time resolved flow field measurements around a realistic rowing oar blade that moves along a realistic path through water. To the authors’ knowledge no prior account of this complex flow field has been given. Simultaneously with the flow field measurements, the hydrodynamic forces acting on the blade were measured. These combined measurements allow us to identify the relevant flow physics that governs rowing propulsion, and subsequently use this information to adjust the oar blade configuration to improve rowing propulsion. Analysis of the instationary flow field around the oar blade during the drive phase indicated how the initial formation, and subsequent development, of leading-edge and trailing-edge vortices are related to the generation of instationary lift and drag forces, and how these forces contribute to rowing propulsion. It is shown that the observed individual flow mechanisms are similar to the flow mechanisms observed in bird flight, but that the overall propulsive mechanism for rowing propulsion is fundamentally different. To quantify the rowing propulsion efficiency, we introduced the energetic efficiency $\eta _E$ and the impulse efficiency $\eta _J$, where the latter can be interpreted as the alignment of the generated impulse with the propulsive direction. It is found that in the conventional oar blade configuration, the generated impulse is not aligned with the propulsive direction, indicating that the propulsion is suboptimal. By adjusting the angle at which the blade is attached to the oar, the generation of leading- and trailing-edge vortices is altered such that the generated impulse better aligns with the propulsive direction, thus increasing the efficiency.

The high-Reynolds-number axisymmetric wake of a slender body with a turbulent boundary layer is investigated using a hybrid simulation. The wake generator is a $6:1$ prolate spheroid and the Reynolds number based on the diameter $D$ is $Re=10^5$. The transition of the wake to a state of complete self-similarity is investigated by looking for the first time into the far field of a slender-body wake. Unlike bluff-body wakes, here the flow is not dominated by vortex shedding in the near wake. Instead, the recirculation region is very small, the near wake is quasi-parallel and is characterised by the presence of broadband turbulence. Until $x/D\approx 20$, the wake decay of a slender body with turbulent boundary layer is very similar to the classic high-$Re$ behaviour, $U_d\sim x^{-2/3}$. Extrapolation of this observation to larger $x/D$ has led to the belief that these wakes decay following the asymptotic $-2/3$ decay law. Our results show, however, that this is not the case and the wake transitions to a faster decay rate once complete self-similarity is achieved. In this later region ($20 < x/D < 80$), mean and turbulence profiles are self-similar. Furthermore, despite the high global and local Reynolds numbers, the classic hypotheses that lead to the well-known decay exponents are not fulfilled. Instead, turbulent dissipation follows a non-equilibrium scaling and a new decay rate $U_d\sim x^{-6/5}$ is observed. The transition from $U_d\sim x^{-2/3}$ to $U_d\sim x^{-6/5}$ is preceded by the dominance of the azimuthal $|m|=1$ mode and the emergence of a large-scale helical structure.

The origin and evolution of the three-dimensional flow structures around a pair of roughness cubes embedded in the inner part of a turbulent channel flow (${\textit{Re}}_{\tau \infty }=2300$, where ${\textit{Re}}_{\tau \infty}$ is the friction Reynolds number of the incoming turbulent channel flow) are measured using microscopic dual-view tomographic holography. The cubes’ height, $a=1$ mm, corresponds to 91 wall units or 3.9 % of the half-channel height. They are aligned in the spanwise direction and separated by a, 1.5a and 2.5a. This paper focuses on the mean flow structure, and the data resolution allows detailed characterization of the open separated regions upstream, along the sides, on top of and behind the cubes, as well as measurements of wall shear stresses from velocity gradients. The flow features a horseshoe vortex, a vortical canopy engulfing each cube, a near wake arch-like vortex and multiple interacting streamwise vortices. Most of the boundary layer vorticity is entrained into the horseshoe vortex. The canopy, consisting of wall-normal vorticity to the sides, and spanwise vorticity on top of the cube, originates from the front surface. The streamwise vortices originate from realignment of the other components along the corners of the front surface. Merging of streamwise structures around and behind each cube causes formation of a large streamwise vortex rotating in the same direction as the inner horseshoe leg, with remnants of the outer leg under it. This merging occurs earlier and the entire flow structure becomes more asymmetric with decreasing spacing. Peaks and minima in the distributions of the wall shear stress are associated with the formation of and interactions among the near-wall vortices.

New analytical solutions for the one-dimensional (1-D) steady-state compressible viscous diabatic flow of an ideal gas through a constant cross-section pipe have been obtained. A constant and a variable heat flux with the walls, the latter being the more relevant for engineering applications, have been considered. To be able to analytically solve the problem, it is essential to determine the correct transformations of the variables and to identify the kinetic energy per unit of mass as the physical variable that appears in the final ordinary differential equation. A dimensionless representation of the analytical solutions, which points out the fundamental role exerted by a few dimensionless groups in problems where viscous power dissipation and heat transfer power are present simultaneously, is also presented. The obtained analytical solutions have successfully been validated for both subsonic and supersonic flows through a comparison with the corresponding numerical time asymptotic solutions of the generalised Euler equations for 1-D gas dynamics problems. The thus validated analytical solutions, which have also been physically discussed, extend Fanno's (1904) and Rayleigh's (1910) models that refer to 1-D steady-state viscous adiabatic and inviscid diabatic flows, respectively.

The dynamics of settling finite-size particles in vertical channel flows of Newtonian and viscoelastic carrier fluids is examined using particle resolved simulations. Comparison with neutrally buoyant particles in the same configuration highlights the effect of settling. The particle volume fraction is $5\,\%$, and a gravity field acts counter to the flow direction. Despite a modest density ratio ($\rho _r = 1.15$), qualitative changes arise due to the relative velocity between the particle and fluid phases. While dense particles are homogeneously distributed in the core of the channel, the mean concentration profile peaks at approximately two particle diameters from the wall due to a competition between shear- and rotation-induced lift forces. These forces act in the cross-stream directions, and are analysed by evaluating conditional averages along individual particle trajectories. The correlation between the angular and translational velocities of the particles highlights the significance of the Magnus lift force in both the spanwise and wall-normal directions. The collective behaviour of the particles is also intriguing. Using a Voronoï analysis, strong clustering is identified in dense particles near the wall, which is shown to alter their streamwise velocities. This clustering is attributed to the preferential transport of aggregated particles towards the wall. The practical implication of the non-uniformity of particle distribution is a significant increase in drag. When the carrier fluid is viscoelastic, the particle migration is enhanced which leads to larger stresses, thus negating the capacity of viscoelasticity to reduce turbulent drag.

We study the possibility of having resonant interactions between three Rossby modes on a coast or channel of arbitrary orientation. A Rossby mode comprises two propagating Rossby waves (RWs) to satisfy the no normal flow through the boundary(ies). In each geometry, we state the conditions, degrees of freedom and RWs of the primary two modes that could force a third mode. We discuss differences between zonal and non-zonal orientations. Resonant interactions are only possible if all RWs participate in the zonal case, while only three RWs participate in the non-zonal case. The non-zonality reduces the degrees of freedom of the resonance conditions, and the solutions are more restrictive for more meridional orientations. In particular, there are no solutions if the coast or channel is meridional. For the non-zonal coast, we find a family of solutions for given periods $T_1$ and $T_2$ of the primary modes. Using multiple scales, we obtain a uniformly valid solution of the quasi-geostrophic potential vorticity equation (QGPVE), with the resonant modes exchanging energy in space. There are no degrees of freedom for the non-zonal channel, and we develop a graphical method to seek resonant solutions, finding some. We provide a bounded solution of the QGPVE in case the primary modes excite one RW, not a channel mode, and the modes do not exchange energy either in time or space. Regarding possible oceanographic applications, we show solutions for the Hawaiian Ridge and inquire if there are solutions in the Mozambique Channel, Tasman Sea, Denmark Strait and the English Channel.

Three-dimensional (3-D) wake transition for flow past a diamond cylinder is investigated numerically. Detailed 3-D direct numerical simulations (DNS) show that the wake is represented by mode A with global vortex dislocations for Reynolds numbers Re = 121–150, followed by a mode swapping between modes A and B for Re = 160–210 and increasingly disordered mode B for Re ≥ 220. In the mode swapping regime, different characteristics of the dislocation and non-dislocation periods are revealed by decomposing flow properties (e.g. the root-mean-square lift coefficient) into the values corresponding to the dislocation and non-dislocation periods. Such decomposition helps to explain some major differences observed for the cases of a diamond and a circular cylinder. In addition to DNS, Floquet stability analyses are conducted to identify the 3-D wake instability modes of a diamond cylinder up to Re = 300. Phase-averaged base flow is used to eliminate the quantitative uncertainties induced by the aperiodic secondary vortex street of the base flow. Interestingly, a subharmonic instability mode is identified at Re ≥ 285, whereas mode B is absent. The origin of the subharmonic mode is explained. The disagreement between the DNS and the Floquet analysis regarding the existence of mode B and the subharmonic mode is also explained. It is found that the natural 3-D flow involves complex interactions between the streamwise and spanwise vortices, as well as between the 3-D wake transition and the two-dimensional base-flow transition, which excite mode B and suppress the subharmonic mode.