Turbulent circular pipe flows subjected to axial system rotation are studied using direct numerical simulations (DNS) for a wide range of rotation numbers of $Ro_b = 0\unicode{x2013}20$ at a fixed Reynolds number. To ensure that energetic turbulent eddy motions are captured at high rotation numbers, long pipes up to $L_z = 180{\rm \pi} R$ are used in DNS. Two types of energy-containing flow structures have been observed. The first type is hairpin structures that are characteristic of the turbulent boundary layer developing over the pipe wall for both non-rotating and axially rotating flows. The second type is Taylor columns forming at moderate and high rotation numbers. Based on the study of two-point autocorrelation coefficients, it is observed that Taylor columns exhibit quasi-periods in both axial and azimuthal directions. According to the premultiplied spectra, Taylor columns feature one single characteristic axial length scale at the moderate rotation numbers but two at high rotation numbers. It is discovered that the axial system rotation suppresses the sweep events systematically and impedes the formation of hairpin structures. As the rotation number is increased, the turbulence kinetic energy held by Taylor columns enhances rapidly associated with significant increases in their axial length scales.

A novel fast-running model is developed to predict the three-dimensional (3-D) distribution of turbulent kinetic energy (TKE) in axisymmetric wake flows. This is achieved by mathematically solving the partial differential equation of the TKE transport using the Green's function method. The developed solution reduces to a double integral that can be computed numerically for a wake prescribed by any arbitrary velocity profile. It is shown that the solution can be further simplified to a single integral for wakes with Gaussian-like velocity-deficit profiles. Wind tunnel experiments were performed to compare model results against detailed 3-D laser Doppler anemometry data measured within the wake flow of a porous disk subject to a uniform free-stream flow. Furthermore, the new model is used to estimate the TKE distribution at the hub-height level of the rotating non-axisymmetric wake of a model wind turbine immersed in a rough-wall boundary layer. Our results show the important impact of operating conditions on TKE generation in wake flows, an effect not fully captured by existing empirical models. The wind-tunnel data also provide insights into the evolution of important turbulent flow quantities such as turbulent viscosity, mixing length and the TKE dissipation rate in wake flows. Both mixing length and turbulent viscosity are found to increase with the streamwise distance. The turbulent viscosity, however, reaches a plateau in the far-wake region. Consistent with the non-equilibrium theory, it is also observed that the normalised energy dissipation rate is not constant, and it increases with the streamwise distance.

This study investigates the flow structures and combustion regimes in an axisymmetric cavity-based scramjet combustor with a total temperature of 1800 K and a high Reynolds number of approximately 1 × 107. The hydroxyl planar laser-induced fluorescence technique, along with the broadband flame emission and CH* chemiluminescence, is employed to visualize the instantaneous flame structure in the optically accessible cavity. The jet-wake flame stabilization mode is observed, with intense heat release occurring in the jet wake upstream of the cavity. A hybrid Reynolds-averaged Navier–Stokes/large-eddy simulation approach is performed for the 0.18-equivalent-ratio case with a pressure-corrected flamelet/progress variable model. The combustion regime is identified mainly in the corrugated or wrinkled flamelet regime (approximately 102 < Da < 104, 103 < Ret < 105 where $Da$ is the Damköhler number and $Re_t$ is the turbulent Reynolds number). The combustion process is jointly dominated by supersonic combustion (which accounts for approximately 58 %) and subsonic combustion, although subsonic combustion has a higher heat release rate (peak value exceeding 1 × 109 J (m3s)−1). A partially premixed flame is observed, where the diffusion flame packages a considerable quantity of twisted premixed flame. The shockwave plays a critical role in generating vorticity by strengthening the volumetric expansion and baroclinic torque term, and it can facilitate the chemical reaction rates through the pressure and temperature surges, thereby enhancing the combustion. Combustion also shows a remarkable effect on the overall flow structures, and it drives alterations in the vorticity of the flow field. In turn, the turbulent flow facilitates the combustion and improves the flame stabilization by enhancing the reactant mixing and increasing the flame surface area.

The causal relevance of local flow conditions in open-channel turbulence is analysed using ensembles of interventional experiments in which the effect of perturbing the flow within a small cell is monitored at some future time. When this is done using the relative amplification of the perturbation energy, causality depends on the flow conditions within the cell before it is perturbed, and can be used as a probe of the flow dynamics. The key scaling parameter is the ambient shear, which is also the dominant diagnostic variable for wall-attached perturbations. Away from the wall, the relevant variables are the streamwise and wall-normal velocities. Causally significant cells are associated with sweeps that carry the perturbation towards the stronger shear near the wall, whereas irrelevant ones are associated with ejections that carry it towards the weaker shear in the outer layers. Causally significant and irrelevant cells are themselves organised into structures that share many characteristics with classical sweeps and ejections, such as forming spanwise pairs whose dimensions and geometry are similar to those of classical quadrants. At the wall, this is consistent with causally significant configurations in which a high-speed streak overtakes a low-speed one, and causally irrelevant ones in which the two streaks pull apart from each other. It is argued that this is probably associated with streak meandering.

Experiments of transitional shock wave–boundary layer interactions (SBLIs) over 6$^\circ$ and 10$^\circ$ compression ramps were performed at Mach number 1.65. The unit Reynolds number was varied by a factor of two between 5.6 million per metre and 11 million per metre. Schlieren flow visualization was performed, and mean flow measurements were made using Pitot probes. Free interaction theory was verified from pressure measurements for all operating conditions. A new non-dimensional parameter was developed for scaling the strength of the imposed shock, which was based on the pressure required to separate a boundary layer. The validity of this new scaling was supported by the reconciliation of large discrepancies in a diverse collection of experimental results on the length scales of transitional interactions. This non-dimensional scaling was also applied to turbulent interactions, where different models were used to determine the pressure required to separate a turbulent boundary layer. Finally, a direct comparison between transitional and turbulent SBLIs was made, which revealed new insights into the evolution of length scales based on the state of the boundary layer.

Modular floating solar farms exhibit periodic open surface coverages due to the strip configuration of floating modules that support the photovoltaic (PV) panels on top. The associated modulations in the surface boundary layer and its turbulence characteristics are investigated in the present study under fully developed open channel flows. Different coverage percentages of 100 % (i.e. full cover), 60 %, 30 % and 0 % (i.e. open surface) were tested and measurements were obtained using particle image velocimetry. The results showed that the turbulence statistics are similar when the coverage decreases from 100 % to 60 %. However, with 30 %, both the turbulence intensities and Reynolds stresses increase substantially, reaching up to 50 % higher compared with the 100 % coverage, and the boundary layer thickness increases by more than 25 %. The local skin friction beneath the openings increases by 50 %. Analysis of spanwise vortices and premultiplied spectra indicates that the periodic coverage elongates the hairpin vortex packets and reduces their inclination angle, imposing limitations on sustainable coherent structures. At 30 %, flow detachment and smaller-scale vortices become dominant, reducing the mean velocities and increasing the turbulence intensities. Decreasing coverage percentage with flow detachment also shifts the energy transfer to higher wavenumbers, increasing energy dissipation and decreasing the bulk flow velocity. The kinetic energy and Reynolds stress carried by very large-scale motions decreases from 40 %–50 % with the 100 % and 60 % coverage to around 30 %–40 % with the 30 % coverage. Further research studies involving spanwise heterogeneity, higher Reynolds number and varying submergence of PV modules are needed for environmental considerations.

A model is formulated of a two-dimensional migrating, or swimming, inviscid bubble in a viscous fluid whose unsteady displacement is caused by the spreading over its surface of an initial distribution of insoluble surfactant. Assuming small capillary and Reynolds numbers, and a linear equation of state giving the surface tension as a function of surfactant concentration, the quasi-steady Stokes flow around the bubble is found analytically and explicit formulas are determined for the time-dependent bubble speed and its final overall displacement. At infinite surface Péclet number this is done using a complex version of the method of characteristics to solve a complex partial differential equation of Burgers type. For a finite non-zero surface Péclet number, the problem is shown to be linearizable by a complex variant of the classical Cole–Hopf transformation. The formulation allows general statements to be made on the bubble speed and its total net displacement in terms of the initial surfactant distribution. A weak finite-time singularity in the surface activity associated with an isolated clean point on the bubble surface is also identified and studied in detail.

We leverage the snap-through response of a bistable origami mechanism to induce a discontinuous evolution of drag with flow speed. The transition between equilibrium states is actuated passively by airflow, and we demonstrate that large shape reconfiguration over a small increment of flow velocity leads to a pronounced and sudden drop in drag. Moreover, we show that systematically varying the geometrical and mechanical properties of the origami unit enables the tuning of this drag discontinuity and the critical speed and loading at which it occurs. Experimental results are supported by a theoretical aeroelastic model, which further guides inverse design to identify the combination of structural origami parameters for targeted drag collapse. This approach sheds light on harnessing origami-inspired mechanisms for efficient passive drag control in a fluid environment, applicable for load alleviation or situations requiring swift transitions in aerodynamic performances.

Developing a model to describe the shock-accelerated cylindrical fluid layer with arbitrary Atwood numbers is essential for uncovering the effect of Atwood numbers on the perturbation growth. The recent model (J. Fluid Mech., vol. 969, 2023, p. A6) reveals several contributions to the instability evolution of a shock-accelerated cylindrical fluid layer but its applicability is limited to cases with an absolute value of Atwood numbers close to $1$, due to the employment of the thin-shell correction and interface coupling effect of the fluid layer in vacuum. By employing the linear stability analysis on a cylindrical fluid layer in which two interfaces separate three arbitrary-density fluids, the present work generalizes the thin-shell correction and interface coupling effect, and thus, extends the recent model to cases with arbitrary Atwood numbers. The accuracy of this extended model in describing the instability evolution of the shock-accelerated fluid layer before reshock is confirmed via direct numerical simulations. In the verification simulations, three fluid-layer configurations are considered, where the outer and intermediate fluids remain fixed and the density of the inner fluid is reduced. Moreover, the mechanisms underlying the effect of the Atwood number at the inner interface on the perturbation growth are mainly elucidated by employing the model to analyse each contribution. As the Atwood number decreases, the dominant contribution of the Richtmyer–Meshkov instability is enhanced due to the stronger waves reverberated inside the layer, leading to weakened perturbation growth at initial in-phase interfaces and enhanced perturbation growth at initial anti-phase interfaces.

We consider the steady flow of a viscoelastic film over an inclined plane featuring periodic trenches normal to the main flow direction. The trenches have a square cross-section and side length 5–8 times the capillary length. Owing to the orientation of the substrate, the film fails to coat the topographical feature entirely, forming a second gas–liquid interface inside the trench and two three-phase contact lines at the points where the free surface meets the wall of the trench. The volume of entrapped air depends on material and flow parameters and geometric conditions. We develop a computational model and carry out detailed numerical simulations based on the finite element method to investigate this flow. We solve the two-dimensional mass and momentum conservation equations using the exponential Phan-Thien & Tanner constitutive model to account for the rheology of the viscoelastic material. Due to the strong nonlinearity, multiple steady solutions possibly connected by turning points forming hysteresis loops, transcritical bifurcations and isolated solution branches are revealed by pseudo-arc-length continuation. We perform a thorough parametric analysis to investigate the combined effects of elasticity, inertia, capillarity and viscosity on the characteristics of each steady flow configuration. The results of our simulations indicate that fluid inertia and elasticity may or may not promote wetting, while shear thinning and hydrophilicity always promote the wetting of the substrate. Interestingly, there are conditions under which the transition to the inertial regime is not smooth, but a hysteresis loop arises, signifying an abrupt change in the film hydrodynamics. Additionally, we investigate the effect of the geometrical characteristics of the substrate, and our results indicate that there is a unique combination of the geometry and viscoelastic properties that either maximizes or minimizes the wetting lengths.

We propose a theoretical method to decompose the solution of a Stokes flow past a body immersed in a confined fluid into two simpler problems, related separately to the two geometrical elements of these systems: (i) the body immersed in the unbounded fluid (represented by its Faxén operators); and (ii) the domain of the confinement (represented by its Stokesian multipoles). Specifically, by using a reflection method, and assuming linear and reciprocal boundary conditions (Procopio & Giona, Phys. Fluids, vol. 36, issue 3, 2024, 032016), we provide the expression for the velocity field, the forces, torques and higher-order moments acting on the body in terms of: (i) the volume moments of the body in the unbounded ambient flow; (ii) the multipoles in the domain of the confinement; (iii) the collection of all the volumetric moments on the body immersed in all the regular parts of the multipoles considered as ambient flows. A detailed convergence analysis of the reflection method is developed. In light of the practical applications, we estimate the truncation error committed by considering only the lower-order moments (thus, truncating the matrices) and the errors associated with the approximated expressions available in the literature for force and torques. We apply the theoretical results to the archetypal hydrodynamic system of a sphere with Navier-slip boundary conditions near a plane wall with no-slip boundary conditions, to determine forces and torques on a translating and rotating sphere as a function of the slip length and of the distance of the sphere from the plane. The hydromechanics of a spheroid is also addressed.

The results of an experimental investigation of smooth-body adverse pressure gradient (APG) turbulent boundary layer flow separation and reattachment over a two-dimensional ramp are presented. These results are part of a larger archival smooth-body flow separation data set acquired in partnership with NASA Langley Research Center and archived on the NASA Turbulence Modeling Resource website. The experimental geometry provides initial canonical turbulent boundary layer growth under nominally zero pressure gradient conditions prior to encountering a smooth, two-dimensional, backward facing ramp geometry onto which a streamwise APG that is fully adjustable is imposed. Detailed surface and off-surface flow field measurements are used to fully characterize the smooth-body APG turbulent boundary layer separation and reattachment at multiple spanwise locations over the ramp geometry. Unsteady aspects of the flow separation are characterized. It is shown that the first and second spatial derivatives of the streamwise static surface pressure profile are sufficient to determine key detachment and reattachment locations. The imposed streamwise APG gives rise to inflectional mean velocity profiles and the associated formation of an embedded shear layer, which is shown to play a dominant role in the subsequent flow development. Similarity scaling is developed for both the mean velocity and turbulent stresses that is found to provide self-similar collapse of profiles for different regions of the ramp flow. Despite the highly non-equilibrium flow environment, a new similarity scaling proved capable of providing self-similar turbulent stress profiles over the full streamwise extent of flow separation and downstream reattachment.

The resolvent analysis reveals the worst-case disturbances and the most amplified response in a fluid flow that can develop around a stationary base state. The recent work by Padovan et al. (J. Fluid Mech., vol. 900, 2020, A14) extended the classical resolvent analysis to the harmonic resolvent analysis framework by incorporating the time-varying nature of the base flow. The harmonic resolvent analysis can capture the triadic interactions between perturbations at two different frequencies through a base flow at a particular frequency. The singular values of the harmonic resolvent operator act as a gain between the spatiotemporal forcing and the response provided by the singular vectors. In the current study, we formulate the harmonic resolvent analysis framework for compressible flows based on the linearized Navier–Stokes equation (i.e. operator-based formulation). We validate our approach by applying the technique to the low-Mach-number flow past an airfoil. We further illustrate the application of this method to compressible cavity flows at Mach numbers of 0.6 and 0.8 with a length-to-depth ratio of $2$. For the cavity flow at a Mach number of 0.6, the harmonic resolvent analysis reveals that the nonlinear cross-frequency interactions dominate the amplification of perturbations at frequencies that are harmonics of the leading Rossiter mode in the nonlinear flow. The findings demonstrate a physically consistent representation of an energy transfer from slow-evolving modes toward fast-evolving modes in the flow through cross-frequency interactions. For the cavity flow at a Mach number of 0.8, the analysis also sheds light on the nature of cross-frequency interaction in a cavity flow with two coexisting resonances.

Spanwise vortex instability and the growth of secondary hairpin-like vortical structures in the wake of an oscillating foil are investigated numerically at Reynolds number 8000 in a range of chord-based Strouhal number ($0.32 \le St_c \le 0.56$). The phase-offset ($\phi$) between the heaving and pitching motion is $\phi = 90^\circ$. The wake at the lowest $St_c$ (0.32) is characterized by a single system of streamwise hairpin-like structures that evolve from the core vorticity outflux of the secondary leading edge vortex (LEV) over the foil boundary. The primary LEV features spanwise dislocations, but it does not reveal substantial changes advecting downstream. Increasing $St_c$ beyond 0.32 reveals that the transition in spanwise instability characterizes the deformation of primary LEV cores, which subsequently transforms to hairpin-like secondary structures. At higher $St_c$, stronger trailing edge vortices (TEVs) grow in close proximity to the primary LEVs, which contributes to an enhanced localized vortex compression and tilting near dislocations. This phenomenon amplifies the undulation amplitude of primary LEVs, eventually leading to vortex tearing. The larger circulation of TEVs with increasing $St_c$ provides an additional explanation for an accelerated vortex compression that coincides with a faster transition of spanwise LEV instability to secondary hairpin-like structures in the wake.

Nonlinear electrokinetic phenomena, where electrically driven fluid flows depend nonlinearly on the applied voltage, are commonly encountered in aqueous suspensions of colloidal particles. A prime example is the induced-charge electro-osmosis, driven by an electric field acting on diffuse charge induced near a polarizable surface. Nonlinear electrohydrodynamic flows also occur in non-polar fluids, driven by the electric field acting on space charge induced by conductivity gradients. Here, we analyse the flows about a charge-neutral spherical solid particle in an applied uniform electric field that arise from conductivity dependence on local field intensity. The flow pattern varies with particle conductivity: while the flow about a conducting particle has a quadrupolar pattern similar to induced-charge electro-osmosis, albeit with opposite direction, the flow about an insulating particle has a more complex structure. We find that this flow induces a force on a particle near an electrode that varies non-trivially with particle conductivity: while it is repulsive for perfectly insulating particles and particles more conductive than the suspending medium, there exists a range of particle conductivities where the force is attractive. The force decays as the inverse square of the distance to the electrode and thus can dominate the dielectrophoretic attraction due to the image dipole, which falls off with the fourth power with the distance. This electrohydrodynamic lift opens new possibilities for colloidal manipulation and driven assembly by electric fields.

Extensive three-dimensional boundary-integral simulations are presented for the steady-state, low-Reynolds-number motion of a non-wetting deformable drop in another liquid on an inclined solid wall. The drop remains separated from the wall by a lubricating film. The boundary-integral formulation is based on the half-space Green function. The focus is on the challenging case of small tilt angles $\theta$ combined with high drop-to-medium viscosity ratios $\lambda$, when the drop travels with strong hydrodynamical interaction very close to the wall. Simulations to steady state have required ultrahigh drop surface resolutions (to $3\times 10^5$ boundary elements) achieved through multipole acceleration and combined with novel regularization to fully eliminate near-singular behaviour of the double-layer integrals due to small clearance. Non-dimensional drop speed $U$ is presented for $\theta \geq 7.5^\circ$, $\lambda \leq 300$ and in a broad range of Bond numbers $B$, covering from nearly spherical to strongly pancaked drops. The results are consistent with published experiments on liquid–liquid systems. At small $\theta$ and $\lambda \gg 1$, $U$ is a strong, decreasing function of $B$; the asymptotic regime $U\to 0$ at $B\to 0$ is not observed in the simulated range. For small $B$, the dimpled thin-film geometry is insensitive to $\lambda =1\unicode{x2013}300$. For pancaked drops, the lubrication film is much thicker for $\lambda =1$ than for $\lambda \gg 1$ drops. Approximate thin-film uniformity in the drop motion direction is confirmed for pancaked, but not for $B\ll 1$, drops. Kinematics of drop motion shows that neither perfect tank treading, nor perfect rolling can be approached for liquid–liquid systems in the purely hydrodynamical formulation. The methodology is applicable to other problems and can allow for direct inclusion of short-range colloidal forces in three-dimensional boundary-integral simulations.

Non-helical turbulence within a linear shear flow has demonstrated efficient amplification of large-scale magnetic fields in numerical simulations, but its precise mechanism remains elusive. The incoherent $\alpha$ mechanism proposes that a zero-mean fluctuating transport coefficient $\alpha$ (linked to kinetic helicity) in the shear flow is a candidate driver. Previous renovating-flow models have proposed that the correlation time of helicity fluctuations must be sufficiently extended to overcome turbulent magnetic diffusivity, yet only empirical validation of this concept has been obtained. In this study, we conduct direct numerical simulations of weakly compressible non-helical hydrodynamic turbulence. We scrutinize the correlation times of velocity and kinetic helicity fluctuations in distinct flow configurations, including rotation, shearing and Keplerian flows, as well as the shearing burgulence counterpart. Our findings indicate that rotation contributes to a prolonged correlation time of helicity compared with velocity, particularly notable in auto-correlations of both volume-averaged quantities and individual Fourier modes due to the formation of large-scale vortices. In contrast, moderate shear strength does not exhibit significant scale separation, with shear flows elongating vortices in the shear direction. Shearing burgulence, characterized by shorter helicity correlation times, appears less conducive to hosting the incoherent $\alpha$ effect. Notably, at modest shear rates, only Keplerian flows exhibit sufficiently coherent helicity fluctuations, in contrast to shearing flows. However, the relative strength of helicity fluctuations compared with turbulent diffusivity is significantly lower, raising doubts about the viability of the incoherent $\alpha$ effect as a potential dynamo driver in the subsonic flows examined in this study.

First predicted by Richtmyer in 1960 and experimentally confirmed by Meshkov in 1969, the Richtmyer–Meshkov instability (RMI) is crucial in fields such as physics, astrophysics, inertial confinement fusion and high-energy-density physics. These disciplines often deal with strong shocks moving through condensed materials or high-pressure plasmas that exhibit non-ideal equations of state (EoS), thus requiring theoretical models with realistic fluid EoS for accurate RMI simulations. Approximate formulae for asymptotic growth rates, like those proposed by Richtmyer, are helpful but rely on heuristic prescriptions for compressible materials. These prescriptions can sometimes approximate the RMI growth rate well, but their accuracy remains uncertain without exact solutions, as the fully compressible RMI growth rate is influenced by both vorticity deposited during shock refraction and multiple sonic wave refractions. This study advances previous work by presenting an analytic, fully compressible theory of RMI for reflected shocks with arbitrary EoS. It compares theoretical predictions with heuristic prescriptions using ideal gas, van der Waals gas and three-term constitutive equations for simple metals, the latter being analysed with detailed and simplified ideal-gas-like EoS. We additionally offer an alternative explicit approximate formula for the asymptotic growth rate. The comprehensive model also incorporates the effects of constant-amplitude acoustic waves at the interface, associated with the D'yakov–Kontorovich instability in shocks.

In Couette flow, the liquid atoms adjacent to a solid substrate may have a finite average tangential velocity relative to the substrate. This so-called slip has been observed frequently. However, the particular molecular-level mechanisms that give rise to liquid slip are poorly understood. It is often assumed that liquid slip occurs by surface diffusion whereby atoms independently move from one substrate equilibrium site to another. We show that under certain conditions, liquid slip is due not to singular independent molecular motion, but to localized nonlinear waves that propagate at speeds that are orders of magnitude greater than the slip velocity at the liquid–solid interface. Using non-equilibrium molecular dynamics simulations, we find the properties of these waves and the conditions under which they are to be expected as the main progenitors of slip. We also provide a theoretical guide to the properties of these nonlinear waves by using an augmented Frenkel–Kontorova model. The new understanding provided by our results may lead to enhanced capabilities of the liquid–solid interface, for heat transfer, mixing, and surface-mediated catalysis.

This paper explores active wake-flow control on a notchback Ahmed body using genetically inspired optimization. Hotwire and particle image velocimetry measurements record velocity data and flow structures in the wake. Pulsed jets at four actuation slots (two at the roof trailing edge, two at the side trailing edges) dynamically control the wake to minimize aerodynamic drag. The study achieves up to 9.2 % (without consideration of energy consumption) drag reduction, primarily by manipulating vortices from the roof rear end. The paper elucidates the underlying flow mechanism and evaluates various actuation strategies, highlighting how optimal control leads to reattachment of wake separation at the rear slant, diminishing the slant bubble and promoting downstream reattachment for enhanced drag reduction.