The high-Strouhal-number pulsatile flow in a curved pipe is studied numerically. A general force analysis is developed for the bend force, where the new contribution from flow acceleration is identified and analysed. The mechanisms of secondary flow production are studied by extending Hawthorne's (Proc. R. Soc. Lond. A, vol. 206, issue 1086, 1951, pp. 374–387) model to account for viscous effects and applied to assess the distinct contributions from an inviscid stretching and no-slip condition. A detailed comparison is made between the numerical simulations and models for a pipe flow characterised by a volume flux $Q=U_b A |\sin \varOmega _p t|$ (where $U_b$ is the maximum bulk velocity, $\varOmega _p$ is the angular frequency and $A$ is the pipe cross-sectional area). For high-Reynolds-number ($Re_b$) and high-Strouhal-number ($St$), the bend force predictions are in good agreement with the numerical results over a wide range of bend curvature ($R_c/D$; where $R_c$ is the bend radius of curvature and $D$ is the pipe diameter) owing to the influence of the streamwise flow acceleration on the pressure field. At high-$St$, the streamwise vorticity (secondary flow) distribution is steady and close to the low-$St$ case, which is explained using a linear secondary flow model.

Interfacial stability is important for many processes involving heat and mass transfer across two immiscible phases. For the evaporation of a binary solution with one component more volatile than the other, gradients in surface tension can arise. These gradients can ultimately destabilize the liquid–gas interface. We study the evaporation of an ethanol–water solution, for which ethanol is more volatile. The solution is contained in a horizontal Hele-Shaw cell which is open from one end to allow for evaporation into air. A Marangoni instability is then triggered at the liquid–air interface. We study the temporal evolution of the instability through its effects on the bulk of the liquid. More specifically, the growth of convective cells is measured with confocal microscopy and the velocity field with microparticle image velocimetry. The results of numerical simulations based on quasi-two-dimensional equations satisfactorily compare with the experimental observations, even without consideration of evaporative cooling, although this cooling can play an extra role in experiments. Furthermore, a linear stability analysis applied to a simplified version of the quasi-two-dimensional equations showed reasonably good agreement with the results from simulations at early times, when the instability has just been triggered and before coarsening. In particular, we find a critical Marangoni number below which a regime of stability is predicted.

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.

This study presents an experimental dataset documenting the evolution of a turbulent boundary layer downstream of a rough-to-smooth surface transition. To investigate the effect of upstream flow conditions, two groups of experiments are conducted. For the Group-Re cases, a nominally constant viscous-scaled equivalent sand grain roughness $k_{s0}^{+}\approx 160$ is maintained on the rough surface, while the friction Reynolds number $Re_{\tau 0}$ ranges from 7100 to 21 000. For the Group-ks cases, $Re_{\tau 0}\approx 14\,000$ is maintained while $k_{s0}^{+}$ ranges from 111 to 228. The wall-shear stress on the downstream smooth surface is measured directly using oil-film interferometry to redress previously reported uncertainties in the skin-friction coefficient recovery trends. In the early development following the roughness transition, the flow in the internal layer is not in equilibrium with the wall-shear stress. This conflicts with the common practise of modelling the mean velocity profile as two log laws below and above the internal layer height, as first proposed by Elliott (Trans. Am. Geophys. Union, vol. 39, 1958, pp. 1048–1054). As a solution to this, the current data are used to model the recovering mean velocity semi-empirically by blending the corresponding rough-wall and smooth-wall profiles. The over-energised large-scale motions leave a strong footprint in the near-wall region of the energy spectrum, the frequency and magnitude of which exhibit dependence on $Re_{\tau 0}$ and $k_{s0}^{+}$, respectively. The energy distribution in near-wall small scales is mostly unaffected by the presence of the outer flow with rough-wall characteristics, which can be used as a surrogate measure to extract the local friction velocity.

A slender trefoil knotted vortex is studied using direct numerical simulation of the Navier–Stokes equations for vortex Reynolds numbers ($Re \equiv \varGamma /\nu$, circulation/viscosity) up to 12 000. For initially zero twist ($T_{w,0}=0$), neither the writhe $W_r$ nor the global helicity $H$ is conserved. Initially $W_r$ slowly decreases, then suddenly drops during reconnection and becomes almost constant thence; its evolution is almost $Re$ independent. Before reconnection, $H$ also gradually decreases but sharply increases during reconnection. The evolution of $H$ after reconnection strongly depends on $Re$. While steadily decreasing at low $Re$, $H$ significantly increases before eventually decaying at high $Re$. Flow visualization, helicity decomposition and helical wave decomposition reveal that significant amounts of positive and negative twist helicities are simultaneously generated before and during reconnection. Also, the small leading and large trailing rings resulting from asymmetric reconnection have respectively negative and positive twists, which then decay differently due to different initial values, geometries and mutual induction. In particular, at high $Re$, the twist in the small ring, under stretching by the large trailing ring, decays much faster and even switches sign to become positive by the writhe-to-twist conversion – the main reason for the ‘transient growth’ of $H$. Simulations with non-zero initial twists ($T_{w,0}=7.48$ and $22.48$) reveal that the overall dynamics is similar to the $T_{w,0}=0$ case. Hence, the evolution of the trefoil knotted vortex is mainly governed by $W_r$, not $T_w$, although the latter is found to play an essential role in enstrophy growth as well as energy cascade.

We address the issue of the generation mechanism of near-wall reverse flow (NWRF) events in a fully developed turbulent duct flow using direct numerical simulations and particle image velocimetry at a relatively low Reynolds number $Re_\tau \simeq 200$. The analysis demonstrates the existence of a large-scale high-momentum flow structure originating upstream of a NWRF region. We propose a conceptual model of the NWRF formation and suggest that they are caused by intensive hairpin vortices incipient at the interface between large-scale high- and low-momentum flow regions identified using a conditional averaging procedure. The similarity of a flow topology associated with the NWRF region for $Re_\tau \simeq 200$ with those for $Re_\tau \simeq 1000$ (Chin et al., Phys. Rev. Fluids, vol. 3, issue 11, 2018, p. 114607) and $550 \leqslant Re_\tau \leqslant 2000$ (Cardesa et al., J. Fluid Mech., vol. 880, 2019) indicates the generality of the proposed mechanism.

We present the dynamics of a hydrofoil free to oscillate in a plane as it interacts with vortices that are shed from a cylinder placed upstream. We consider cases where the cylinder is (i) fixed, (ii) forced to rotate constantly in one direction or (iii) forced to rotate periodically. When the upstream cylinder is fixed, at lower reduced velocities, the hydrofoil oscillates with a frequency equal to the frequency of vortices shed from the cylinder, and at higher reduced velocities with a frequency equal to half of the shedding frequency. When we force the cylinder to rotate in one direction, we control its wake and directly influence the response of the hydrofoil. When the rotation rate goes beyond a critical value, the vortex shedding in the cylinder's wake is suppressed and the hydrofoil is moved to one side and remains mainly static. When we force the cylinder to rotate periodically, we control the frequency of vortex shedding, which will be equal to the rotation frequency. Then at lower rotation frequencies, the hydrofoil interacts with one of the vortices in its oscillation path in the positive crossflow (transverse) direction, and with the second vortex in the negative crossflow direction, resulting in a 2:1 ratio between its inline and crossflow oscillations and a figure-eight trajectory. At higher rotation frequencies, the hydrofoil interacts with both shed vortices on its positive crossflow path and again in its negative crossflow path, resulting in a 1:1 ratio between its inline and crossflow oscillations and a linear trajectory.

We study a turbulent jet issuing from a cylindrical nozzle to characterise coherent structures evolving in the turbulent boundary layer. The analysis is performed using data from a large-eddy simulation of a Mach 0.4 jet. Azimuthal decomposition of the velocity field in the nozzle shows that turbulent kinetic energy predominantly resides in high azimuthal wavenumbers; the first three azimuthal wavenumbers, that are important for sound generation, contain much lower, but non-zero amplitudes. Using two-point statistics, low azimuthal modes in the nozzle boundary layer are shown to exhibit significant correlations with modes of the same order in the free-jet region. Spectral proper orthogonal decomposition is used to distill a low-rank approximation of the flow dynamics. This reveals the existence of tilted coherent structures within the nozzle boundary layer and shows that these are coupled with wavepackets in the jet. The educed nozzle boundary-layer structures are modelled using a global resolvent analysis of the mean flow inside the nozzle to determine the most amplified flow responses using the linearised Navier–Stokes system. It is shown that the most-energetic nozzle structures can be successfully described with optimal resolvent response modes, whose associated forcing modes are observed to tilt against the nozzle boundary layer, suggesting that the Orr mechanism underpins these organised, turbulent, boundary-layer structures.

We consider the rotating and translating equilibria of open finite vortex sheets with endpoints in two-dimensional potential flows. New results are obtained concerning the stability of these equilibrium configurations which complement analogous results known for unbounded, periodic and circular vortex sheets. First, we show that the rotating and translating equilibria of finite vortex sheets are linearly unstable. However, while in the first case unstable perturbations grow exponentially fast in time, the growth of such perturbations in the second case is algebraic. In both cases the growth rates are increasing functions of the wavenumbers of the perturbations. Remarkably, these stability results are obtained entirely with analytical computations. Second, we obtain and analyse equations describing the time evolution of a straight vortex sheet in linear external fields. Third, it is demonstrated that the results concerning the linear stability analysis of the rotating sheet are consistent with the infinite aspect ratio limit of the stability results known for Kirchhoff's ellipse (Love, Proc. Lond. Math. Soc., vol. s1–25, 1893, pp. 18–43; Mitchell & Rossi, Phys. Fluids, vol. 20, 2008, p. 054103) and that the solutions we obtained accounting for the presence of external fields are also consistent with the infinite aspect ratio limits of the analogous solutions known for vortex patches.

The question of how finite-amplitude, small-scale topography affects small-amplitude motions in the ocean is addressed in the framework of the rotating shallow water equations. The extent to which the dispersion relations of Poincaré, Kelvin and Rossby waves are modified in the presence of topography is illuminated, using a range of numerical and analytical techniques based on the method of homogenisation. Both random and regular periodic arrays of topography are considered, with the special case of regular cylinders studied in detail, because this case allows for highly accurate analytical results. The results show that, for waves in a $\beta$-channel bounded by sidewalls, and for steep topographies outside of the quasi-geostrophic regime, topography acts to slow Poincaré waves slightly, Rossby waves are slowed significantly and Kelvin waves are accelerated for long waves and slowed for short waves, with the two regimes being separated by a narrow band of resonant wavelengths. The resonant band, which is due to the excitation of trapped topographic Rossby waves on each seamount, may affect any of the three wave types under the right conditions, and for physically reasonable results requires regularisation by Ekman friction. At larger topographic amplitudes, for cylindrical topography, a simple and accurate formula is given for the correction to the Rossby wave dispersion relation, which extends previous results for the quasi-geostrophic regime.

Full flow-field data derived from a direct numerical simulation for channel flow subjected to drag-reducing oscillatory spanwise motion are analysed by means of a recently developed methodology, which consolidates the entire simulation data set within multiple-variable joint-probability-density functions (PDFs). A wide variety of statistical data of interest are then extracted from the joint PDF without recourse to any of the original simulation data. The nominal friction Reynolds number of the baseline (unactuated) flow is 1025, and the actuation is effected at a wall-scaled period of 100, at which value the drag-reduction level is approximately 30 %, while any actuation-induced phase fluctuations in the streamwise direction are minimal. Interest focuses on the elucidation of the mechanisms by which the near-wall turbulence is modified by the action of footprints of large-scale structures in the outer parts of the log-law region, which tend to intensify as the Reynolds number rises. To elucidate these mechanisms, the Reynolds stresses and their production rates, conditional on the intensity of large-scale skin-friction fluctuations, are examined. The investigation includes a separation of the Reynolds stresses into large-scale and small-scale components by means the empirical mode decomposition, allowing the intensity of footprinting and of small-scale modulation of the near-wall turbulence to be quantified separately. The conditional statistical properties are presented in the form of maps in planes having the wall-normal distance and large-scale skin friction as coordinates, supplemented by wall-normal property profiles and an examination of large-scale and small-scale contributions to the skin friction. The analysis highlights the strongly asymmetric response of the production rate and the turbulence level in the buffer layer to positive vs. negative footprints, the former strongly enhancing small-scale turbulence. This is proposed to be at least a partial explanation of the decline in the drag-reduction effectiveness of oscillatory spanwise wall motion with increasing Reynolds number.

This study investigates water waves generated by a bottom obstacle translating at a subcritical speed in constant water depth, using a combination of analytical and numerical approaches. The newly derived analytical solutions reveal two types of waves – the transient free waves that propagate radially outwards, and the trapped wave that stays on top of the translating bottom obstacle. Closed-form asymptotic solutions for both the free surface and the flow velocities are derived in the far field, and near the leading wave or in the shallow water limit. The far-field leading waves are mathematically shown to be insensitive to the exact shape of the obstacle. Numerical long-wave models are employed to examine effects unaccountable by the linear analytical solutions. Nonlinear effects are found to cause only small deviations from the linear solutions. The effects of the obstacle's acceleration and deceleration are also examined numerically. Overall, the idealised linear analytical solutions predict well the characteristics of water waves generated by a bottom obstacle, and therefore can serve as the cornerstone of a theory-based model for quickly predicting the tsunamis generated by a submarine landslide.

Hypersonic flows over a compression ramp with different leading-edge radii are numerically investigated. Flow separation occurs on the cold-wall compression ramp with a free-stream Mach number of 7.7 and a unit Reynolds number of $4.2 \times 10^6$ m$^{-1}$. By performing direct numerical simulations (DNS), it is shown that the separation bubble enlarges when the leading-edge radius is increased from zero up to a critical value. Beyond the critical radius, the separation bubble conversely shrinks as the radius is further increased. Global stability analysis (GSA) is employed to investigate the three-dimensional instability of the two-dimensional base flows. It is found that the inherent instability in the flow field also exhibits a reversal trend, that is, the flow system firstly becomes more unstable and then tends to be more stable with increasing leading-edge radius. The growth rate and spanwise wavelength of the unstable modes identified by GSA are verified by DNS. Accompanying the occurrence of three-dimensionality, streamwise heat-flux streaks are formed on the ramp surface downstream of reattachment. The present study demonstrates that a proper blunting of the leading edge can suppress flow separation, reduce aerodynamic heating and stabilise the flow system for a hypersonic compression-ramp flow.

A single-time two-point spectral closure is developed by approximation of the Lagrangian direct interaction approximation (LDIA) for a passive scalar in the presence of a mean scalar gradient in homogeneous isotropic turbulence. In the derivation of a single-time two-point spectral closure, the two assumptions, Markovianisation and the exponential form of Lagrangian velocity response function, are made for the LDIA, and angle dependence of the passive-scalar field is expressed by the second-order truncation of Legendre polynomials, in which such a truncation is justified by the linear theory. The resulting closure equations are derived in a straightforward way except for the above assumptions and further simplifications. The closures studied agree qualitatively with direct numerical simulation for one- and two-point statistics of a passive-scalar field in the case of unity Schmidt number. For both direct numerical simulation and closures, we show that the dependence of one-point passive-scalar statistics on the Péclet number based on scalar Taylor microscales collapses properly compared with that based on velocity microscales. We also propose universal scaling laws for second-order scalar structure functions and demonstrate their validity.

A cylinder undergoes precession when it rotates around its axis and this axis itself rotates around another axis. In a precessing cylinder full of fluid, a steady and axisymmetric component of the azimuthal flow is generally present. This component is called a zonal flow. Although zonal flows have been often observed in experiments and numerical simulations, their origin has eluded theoretical approaches so far. Here, we develop an asymptotic analysis to calculate the zonal flow forced in a resonant precessing cylinder, that is when the harmonic response is dominated by a single Kelvin mode. We find that the zonal flow originates from three different sources: (1) the nonlinear interaction of the inviscid Kelvin mode with its viscous correction; (2) the steady and axisymmetric response to the nonlinear interaction of the Kelvin mode with itself; and (3) the nonlinear interactions in the end boundary layers. In a precessing cylinder, two additional sources arise due to the equatorial Coriolis force and the forced shear flow; however, they cancel exactly. The study thus generalises to any Kelvin mode, forced by precession or any other mechanism. The present theoretical predictions of the zonal flow are confirmed by comparison with numerical simulations and experimental results. We also show numerically that the zonal flow is always retrograde in a resonant precessing cylinder ($m=1$) or when it results from resonant Kelvin modes of azimuthal wavenumbers $m=2$, $3$ and, presumably, higher.

We study the asymptotic behaviour of convective heat transfer for turbulent flows in high-porosity fluid-saturated media by two-dimensional high-resolution numerical simulation. The generalized Navier–Stokes equations for incompressible fluid flow and the heat transport equation in porous media at the representative element volume scale are solved by the lattice Boltzmann method, wherein the non-Darcian effects are taken into consideration. The asymptotic behaviour of the Nusselt number $N$ has been revealed for Rayleigh numbers $10^4\leq R\leq 10^{11}$ and Darcy numbers $10^{-6}\leq \xi \leq 10^6$: all the data for various Darcy numbers gradually collapse onto a unique line with increasing Rayleigh number. The asymptote can be well represented by $N=0.146\times R^{0.286}$ for $R>2\times 10^7$, which approaches the relationship for the Rayleigh–Bénard turbulent convection of free fluid flows. The transition can be characterized by a scaling analysis with $R^{}\xi ^{3/2}\sim 1$, below which, however, the data collapse onto the Darcy limit for porous media. The Reynolds number and the Nusselt number both increase with Darcy number above the onset of convection, whereas a premature saturation of the Nusselt number is observed in comparison with that of the Reynolds number. The counter-gradient heat transport by the large-scale flows is quantified, which compensates for the increase of the gradient heat transport with Darcy number. The heat transfer in high-porosity fluid-saturated media with a very small Darcy number $\xi \geq 10^{-6}$ can be comparable to that of free fluid flows for a sufficiently high Rayleigh number $R\geq 10^{11}$.

We explore the strong stratification regime of stably stratified turbulence and the intermediate regime towards the viscosity-affected stratified state. Three-dimensional velocity-density fields from direct numerical simulations are decomposed into internal gravity waves (IGWs) and eddy motion based on Riley's decomposition (Riley et al., AIP Conf. Proc., vol. 76, issue 1, 1981, pp. 79–112) extended to account for the space–time properties of waves, their modification by vertically sheared horizontal flow and the vertical mixing by eddies (Lam et al., Atmosphere, vol. 11, issue 4, 2020, p. 420). We establish the evolution equations for the IGW and eddy parts separately. Up to buoyancy Reynolds number ${Re}_b\sim 1$, we observe a large exchange of energy that pumps energy from the IGW to eddy. For ${Re}_b>1$, the IGW and eddy dynamics seem to be separate and no global exchange is observed. Our decomposition enables computation of the contributions to the mixing coefficient in terms of the IGW and eddy. At the largest ${Re}_b$ considered, the mixing due to eddies is four times that due to waves.

Soft substrates, omnipresent in several fundamental processes ranging from the tribological to biophysical, are often subjected to viscous fluid-mediated dynamic loading for their real-time monitoring, by employing advanced characterization tools in the forms of different surface probing apparatus. Here, we bring out exclusive facets of the two-way interplay between large-amplitude loading of a proximal rigid spherical probe on a soft substrate coating and the combined consequences of electrostatic and van der Waals interactions (modelled as Derjaguin–Landau–Verwey–Overbeek (DVLO) forces) on the same. Our results reveal that for high-frequency oscillatory loading and large amplitude of probe motion, the DLVO interactions do not appreciably affect the force response. On the other hand, for low-frequency high-amplitude oscillatory loading, DLVO effects are shown to magnify the substrate deformation tenfold and the force response by up to two orders of magnitude, in experimentally tractable physical limits. Additionally, we find that compressibility of substrate material increases its deformation by approximately a factor of two. Because of the exact shape of the deformable surface as well as the sphere–substrate separation distance being unknown at every time instant a priori, estimation of the resultant force interactions by simply employing an algebraic linear superposition of the different force components is shown to be inappropriate for characterizing the interactions of a highly compliant substrate in close proximity to the dynamically modulated probe. These results may turn out to be of profound importance in rationalizing the interpretation of surface force measurements on soft substrates in several applications encompassing engineering and nano-bio technology.

The rotation applied to a circular cylinder, rigidly mounted in a current perpendicular to its axis, can result in the suppression of vortex shedding and of the associated force fluctuations. It also causes the emergence of a myriad of two- and three-dimensional flow regimes. The present paper explores numerically the impact of a deviation from the normal incidence configuration, by considering a rotating cylinder inclined in the current. The Reynolds number based on the body diameter and the magnitude of the current velocity component normal to its axis ($U_\perp$) is set to $100$. The range of values of the rotation rate (ratio between body surface velocity and $U_\perp$, $\alpha \in [0,5.5]$) encompasses the two unsteady flow regions and three-dimensional transition identified at normal incidence. The inclination angle ($\theta$) refers to the angle between the current direction and the plane perpendicular to the cylinder axis. A low inclination angle ($\theta \in \{15^\circ ,30^\circ \}$), i.e. slight deviation from normal incidence ($\theta =0^\circ$), has a limited influence on the global evolution of the flow with $\alpha$, which can be predicted via the independence principle (IP), based on $U_\perp$ only. This highlights the robustness of prior observations made for $\theta =0^\circ$. Some effects of the axial flow are, however, uncovered in the high-$\alpha$ range; in particular, the single-sided vortex shedding is replaced by an irregular streamwise-oriented structure. In contrast, a large inclination angle ($\theta =75^\circ$) leads to a major reorganization of flow evolution scenario over the entire $\alpha$ range, with the disappearance of all steady regimes, the occurrence of structures reflecting the pronounced asymmetry of the configuration (oblique shedding, strongly slanted vorticity tongues) and a dramatic departure of fluid forces from the IP prediction.

Fluid–fluid displacement in porous media has been viewed through the lens of Lenormand's phase diagram since the late 1980s. This diagram suggests that the character of the flow is controlled by two dimensionless parameters: the capillary number and the viscosity ratio. It is by now well known, however, that the wettability of the system plays a key role in determining the pore-scale displacement mechanisms and macroscopic invasion patterns. Here, we endow Lenormand's diagram with the impact of wettability using dynamic and quasi-static pore-network models. By using the fractal dimension and the ratio of characteristic viscous and capillary pressures we delineate the five principal displacement regimes within the extended phase diagram: stable displacement, viscous fingering, invasion percolation, cooperative pore filling and corner flow. We discuss the results in the context of pattern formation, displacement-front dynamics, pore-scale disorder and displacement efficiency.