At low Reynolds numbers, axisymmetric ellipsoidal particles immersed in a shear flow undergo periodic tumbling motions known as Jeffery orbits, with the orbit determined by the initial orientation. Understanding this motion is important for predicting the overall dynamics of a suspension. While slender fibres may follow Jeffery orbits, many such particles in nature are neither straight nor rigid. Recent work exploring the dynamics of curved or elastic fibres have found Jeffery-like behaviour along with chaotic orbits, decaying orbital constants and cross-streamline drift. Most work focuses on particles with reflectional symmetry; we instead consider the behaviour of a composite asymmetric slender body made of two straight rods, suspended in a two-dimensional shear flow, to understand the effects of the shape on the dynamics. We find that for certain geometries the particle does not rotate and undergoes persistent drift across streamlines, the magnitude of which is consistent with other previously identified forms of cross-streamline drift. For this class of particles, such geometry-driven cross-streamline motion may be important in giving rise to dispersion in channel flows, thereby potentially enhancing mixing.

Microvortex generators are passive control devices smaller than the boundary layer thickness that energise the boundary layer to prevent flow separation with limited induced drag. In this work, we use direct numerical simulations (DNS) to investigate the effect of the Reynolds number in a supersonic turbulent boundary layer over a microramp vortex generator. Three friction Reynolds numbers are considered, up to $Re_\tau = 2000$, for fixed free stream Mach number $M_\infty =2$ and fixed relative height of the ramp with respect to the boundary layer thickness. The high-fidelity data set sheds light on the instantaneous and highly three-dimensional organisation of both the wake and the shock waves induced by the microramp. The full access to the flow field provided by DNS allows us to develop a qualitative model of the near wake, explaining the internal convolution of the Kelvin–Helmholtz vortices around the low-momentum region behind the ramp. The overall analysis shows that numerical results agree excellently with recent experimental measurements in similar operating conditions and confirms that microramps effectively induce a significantly fuller boundary layer even far downstream of the ramp. Moreover, results highlight significant Reynolds number effects, which in general do not scale with the ramp height. Increasing Reynolds number leads to enhanced coherence of the typical vortical structures in the field, faster and stronger development of the momentum deficit region, increased upwash between the primary vortices from the sides of the ramp – and thus increased lift-up of the wake – and faster transfer of momentum towards the wall.

We investigate the effect of inertial particles dispersed in a circular patch of finite radius on the stability of a two-dimensional Rankine vortex in semi-dilute dusty flows. Unlike the particle-free case where no unstable modes exist, we show that the feedback force from the particles triggers a novel instability. The mechanisms driving the instability are characterized using linear stability analysis for weakly inertial particles and further validated against Eulerian–Lagrangian simulations. We show that the particle-laden vortex is always unstable if the mass loading $M>0$. Surprisingly, even non-inertial particles destabilize the vortex by a mechanism analogous to the centrifugal Rayleigh–Taylor instability in radially stratified vortex with density jump. We identify a critical mass loading above which an eigenmode $m$ becomes unstable. This critical mass loading drops to zero as $m$ increases. When particles are inertial, modes that fall below the critical mass loading become unstable, whereas modes above it remain unstable but with lower growth rates compared with the non-inertial case. Comparison with Eulerian–Lagrangian simulations shows that growth rates computed from simulations match well the theoretical predictions. Past the linear stage, we observe the emergence of high-wavenumber modes that turn into spiralling arms of concentrated particles emanating out of the core, while regions of particle-free flow are sucked inward. The vorticity field displays a similar pattern which leads to the breakdown of the initial Rankine structure. This novel instability for a dusty vortex highlights how the feedback force from the disperse phase can induce the breakdown of an otherwise resilient vortical structure.

Turbine–wake and farm–atmosphere interactions influence wind farm power production. For large offshore farms, the farm–atmosphere interaction is usually the more significant effect. This study proposes an analytical model of the ‘momentum availability factor’ to predict the impact of farm–atmosphere interactions. It models the effects of net advection, pressure gradient forcing and turbulent entrainment, using steady quasi-one-dimensional flow assumptions. Turbulent entrainment is modelled by assuming self-similar vertical shear stress profiles. We used the model with the ‘two-scale momentum theory’ to predict the power of large finite-sized farms. The model compared well with existing results of large-eddy simulations of finite wind farms in conventionally neutral boundary layers. The model captured most of the effects of atmospheric boundary layer (ABL) height on farm performance by considering the undisturbed vertical shear stress profile of the ABL as an input. In particular, the model predicted the power of staggered wind farms with a typical error of 5 % or less. The developed model provides a novel way of predicting instantly the power of large wind farms, including the farm blockage effects. A further simplification of the model to predict analytically the ‘wind extractability factor’ is also presented. This study provides a novel framework for modelling farm–atmosphere interactions. Future studies can use the framework to better model large wind farms.

The Naval Research Laboratory ‘Mag Noh problem’, described in this paper, is a self-similar magnetized implosion flow, which contains a fast magnetohydrodynamic (MHD) outward propagating shock of constant velocity. We generalize the classic Noh (OSTI Tech. Rep. 577058, 1983) problem to include azimuthal and axial magnetic fields as well as rotation. Our family of ideal MHD solutions is five parametric, each solution having its own self-similarity index, gas gamma, magnetization, the ratio of axial to the azimuthal field and rotation. While the classic Noh problem must have a supersonic implosion velocity to create a shock, our solutions have an interesting three-parametric special case with zero initial velocity in which magnetic tension, instead of implosion flow, creates the shock at $t=0+$. Our self-similar solutions are indeed realized when we solve the initial value MHD problem with the finite volume MHD code Athena. We numerically investigated the stability of these solutions and found both stable and unstable regions in parameter space. Stable solutions can be used to test the accuracy of numerical codes. Unstable solutions have also been widely used to test how codes reproduce linear growth, transition to turbulence and the practically important effects of mixing. Now we offer a family of unstable solutions featuring all three elements relevant to magnetically driven implosions: convergent flow, magnetic field and a shock wave.

Through direct numerical simulations we investigate the effects of spatiotemporal intermittency as a result of stable stratification in surface heated stratified open channel flow. By adapting the density inversion criterion method of Portwood et al. [J. Fluid Mech., vol. 807, 2016, R2] for our flow, we demonstrate that the flow may be robustly separated into regions of active turbulence for which $Re_B \gtrsim {O}(10)$ and surrounding quiescent fluid, where $Re_B$ is the buoyancy Reynolds number. The intermittency in the flow spontaneously manifests as a deformed horizontal interface between the upper quiescent and lower turbulent flow, characterised by vigorous mixing from ‘overturning’ shear instabilities. The resulting vertical intermittency profile is accurately predicted by a local Monin–Obukhov length normalised by viscous wall units $\varLambda ^+$ such that the flow displays intermittency within the parameter range of $2.5 \lesssim \varLambda ^+ \lesssim 260$. By considering conditional averages of the ‘turbulent’ and ‘quiescent’ flow separately, we find the ‘turbulent’ flow within this region to be described by constant critical gradient Richardson and turbulent Froude numbers of $Ri_{g,c} \approx 0.2$ and $Fr_c \approx 0.3$. We find that the turbulent flow continues to display a $\varGamma \sim Fr^{-1}$ relationship when $Fr < Fr_c$, whereas the quiescent flow shows no correlation between $\varGamma$ and $Fr$, where $\varGamma$ is the flux coefficient. Hence, we demonstrate directly that for our flow, the emergence of an asymptotic ‘saturated’ $\varGamma$ regime in the limit of a low ‘global’ $Fr$ occurs due to intermittency and increasing contributions to measurements of $\varGamma$ from the quiescent flow.

We prove a new rigorous upper bound on the vertical heat transport for Bénard–Marangoni  convection of a two- or three-dimensional fluid layer with infinite Prandtl number. Precisely, for Marangoni number $Ma\gg 1$ the Nusselt number $Nu$ is bounded asymptotically by $Nu\leqslant \text{const.}\times Ma^{2/7}(\ln Ma)^{-1/7}$. Key to our proof are a background temperature field with a hyperbolic profile near the fluid’s surface and new estimates for the coupling between temperature and vertical velocity.

Passive heat transfer enhancement by spanwise rollers associated with the Kelvin–Helmholtz instability was studied through direct numerical simulations of high-aspect-ratio longitudinal ribs at the friction Reynolds number $300$. The temperature was treated as a passive scalar with Prandtl number unity to discuss the similarity between the heat and momentum transfer. The results reveal that the high-aspect-ratio longitudinal ribs lead to a favourable breakdown of the Reynolds analogy, that is, the enhancement of the heat transfer rate surpasses that of the frictional resistance. The favourable breakdown of the Reynolds analogy can be attributed to the enhanced turbulent heat flux compared with the Reynolds shear stress, whereas the rib-induced secondary flow plays a role in reducing the favourable breakdown of the Reynolds analogy. The conditional average statistics reveal that the high-pressure region accompanied by the spanwise rollers suppresses the spanwise roller-induced sweep and ejection motions, leading to smaller Reynolds shear stress than for the turbulent heat flux.

Liquid-infused surfaces can reduce friction drag in both laminar and turbulent flows. However, the heat transfer properties of such multi-phase surfaces have still not been investigated to a large extent. We use numerical simulations to study conjugate heat transfer of liquid-filled grooves. It is shown that heat transfer can increase for both laminar and turbulent liquid flows due to recirculation in the surface texture. Laminar flow simulations show that for the increase to be substantial, the thermal conductivity of the solid must be similar to the thermal conductivity of the fluids, and the recirculation in the grooves must be sufficiently strong (Péclet number larger than 1). The ratio of the surface cavity to the system height is an upper limit of the direct contribution from the recirculation. While this ratio can be significant for laminar flows in microchannels, it is limited for turbulent flows, where the system scale (e.g. channel height) usually is much larger than the texture height. However, heat transfer enhancement of the order of $10\,\%$ is observed (with a net drag reduction) in a turbulent channel flow at a friction Reynolds number ${{Re}}_\tau \approx 180$. It is shown that the turbulent convection in the bulk can be enhanced indirectly from the recirculation in the grooves.

An analytical framework is proposed to explore the structure and kinematics of iso-scalar fields. It is based on a two-point statistical analysis of the phase indicator field which is used to track a given iso-scalar volume. The displacement speed of the iso-surface, i.e. the interface velocity relative to the fluid velocity, is explicitly accounted for, thereby generalizing previous two-point equations dedicated to the phase indicator in two-phase flows. Although this framework applies to many transported quantities, we here focus on passive scalar mixing. Particular attention is paid to the effect of Reynolds (the Taylor based Reynolds number is varied from 88 to 530) and Schmidt numbers (in the range 0.1 to 1), together with the influence of flow and scalar forcing. It is first found that diffusion in the iso-surface tangential direction is predominant, emphasizing the primordial influence of curvature on the displacement speed. Second, the appropriate normalizing scales for the two-point statistics at either large, intermediate and small scales are revealed and appear to be related to the radius of gyration, the surface density and the standard deviation of mean curvature, respectively. Third, the onset of an intermediate ‘scaling range’ for the two-point statistics of the phase indicator at sufficiently large Reynolds numbers is observed. The scaling exponent complies with a fractal dimension of 8/3. A scaling range is also observed for the transfer of iso-scalar fields in scale space whose exponent can be estimated by simple scaling arguments and a recent closure of the Corrsin equation. Fourth, the effects of Reynolds and Schmidt numbers together with flow or scalar forcing on the different terms of the two-point budget are highlighted.

The effect of a nozzle on the wake dynamics of a four-bladed propeller operating in an oblique flow is investigated via modal decomposition and flow visualization of the results obtained from numerical simulations using delayed detached eddy simulations. The wake characteristics and destabilization mechanisms of a non-ducted propeller (NP) and ducted propeller (DP) in axisymmetric and oblique flow conditions are systematically analysed. The wake characteristics on the windward side are very different from those on the leeward side in an oblique flow, and the nozzle has a crucial role in mitigating the asymmetry and weakening the wake deflection. More destabilization mechanisms are present in an oblique flow than in an axisymmetric flow, including the asymmetric evolution and destabilization of the helixes on the windward and leeward sides of the NP wake, the interaction between the vortex shedding and the helixes in the DP leeward region, and the generation of a tube-shaped wake envelope around the nozzle and its rolling-up. Moreover, the effect of the nozzle on wake meandering is discussed based on modal analysis.

The interaction between forward-facing steps of several heights and a pre-existing critical stationary crossflow instability of a swept-wing boundary layer is analysed. Direct numerical simulations (DNS) are performed of the incompressible three-dimensional laminar base flow and the stationary distorted flow that arise from the interaction between an imposed primary stationary crossflow perturbation and the steps. These DNS are complemented with solutions of the linear and the nonlinear parabolised stability equations, used towards identifying the influence of linearity and non-parallelism near the step. A fully stationary solution of the Navier–Stokes equations is enforced numerically, in order to isolate the mechanisms pertaining to the interaction of the stationary disturbance with the step. Results provide insight into the salient modifications of the base laminar boundary layer due to the step, and the response of the incoming crossflow instability to these changes. The fundamental spanwise Fourier mode of the disturbance field gradually lifts up as it approaches the step and passes over it. The flow environment around the step is characterised by a sudden spanwise modulation of the base-flow streamlines. Additional stationary perturbation structures are induced at the step, which manifest in the form of spanwise-aligned velocity streaks near the wall. Shortly downstream of the step, the fundamental component of the crossflow perturbation maintains a rather constant amplification for the smallest steps studied. For the largest step, however, the fundamental crossflow perturbation is stabilised significantly shortly downstream of the largest step. This surprising result is ascribed to a modulation of the kinetic energy transfer between the base flow and the fundamental perturbation field, which is brought forward as a new step interaction mechanism. Possible non-modal growth effects at the step are discussed. Furthermore, the results from DNS indicate significant amplification of the high-order harmonic crossflow components downstream of the step.

We present a theoretical asymptotic solution for high-speed transient flow through microporous media in this work by addressing the inertia effect in the high-pressure-difference pulse-decay process. The capillaric model is adopted, in which a bundle of straight circular tubes with a high length–radius ratio is used to represent the internal flow paths of microporous media so that the flow is described by a simplified incompressible Navier–Stokes equation based on the mean density, capturing the major characteristics of mass flow rate. By order-of-magnitude analysis and asymptotic perturbation, the inertial solution with its dimensionless criterion for the high-pressure-difference pulse-decay process is derived. To be compared with experimental data, the theoretical solution involves all three related effects, including the inertia effect, the slippage effect and the compressibility effect. A self-built experimental platform is therefore established to measure the permeability of microporous media by both pulse-decay and steady-state methods to validate the theoretical solution. The results indicate that the relative difference between two methods is less than 30 % even for permeability at as low as $48.2$ nD $(10^{-21}\,{\rm m}^2)$, and the present theoretical solution can accurately capture the inertia effect in the high-pressure-difference pulse-decay process, which significantly accelerates the measurements for ultra-low-permeability samples.

Two common definitions of the spatially local rate of kinetic energy cascade at some scale $\ell$ in turbulent flows are (i) the cubic velocity difference term appearing in the ‘scale-integrated local Kolmogorov–Hill’ equation (structure-function approach), and (ii) the subfilter-scale energy flux term in the transport equation for subgrid-scale kinetic energy (filtering approach). We perform a comparative study of both quantities based on direct numerical simulation data of isotropic turbulence at Taylor-scale Reynolds number 1250. While in the past observations of negative subfilter-scale energy flux (backscatter) have led to debates regarding interpretation and relevance of such observations, we argue that the interpretation of the local structure-function-based cascade rate definition is unambiguous since it arises from a divergence term in scale space. Conditional averaging is used to explore the relationship between the local cascade rate and the local filtered viscous dissipation rate as well as filtered velocity gradient tensor properties such as its invariants. We find statistically robust evidence of inverse cascade when both the large-scale rotation rate is strong and the large-scale strain rate is weak. Even stronger net inverse cascading is observed in the ‘vortex compression’ $R>0$, $Q>0$ quadrant, where $R$ and $Q$ are velocity gradient invariants. Qualitatively similar but quantitatively much weaker trends are observed for the conditionally averaged subfilter-scale energy flux. Flow visualizations show consistent trends, namely that spatially, the inverse cascade events appear to be located within large-scale vortices, specifically in subregions when $R$ is large.

Two-dimensional oblique detonation wave (ODW) propagations in partially prevaporized n-heptane sprays are numerically simulated with a skeletal chemical mechanism. The influences of the droplet diameter and total equivalence on oblique detonation are considered. The initiation length is found to increase first and then decrease with increasing initial droplet diameter, and the effect of droplet size is maximized when the initial droplet diameter is approximately $10\ \mathrm {\mu } {\rm m}$. As the initial droplet diameter varies, unsteady and steady ODWs are observed. In the cases of unsteady ODWs, temperature gradients and non-uniform distributions of the reactant mixture due to droplet evaporation lead to formation of unsteady detonation propagation, therefore leading to fluctuations in the initiation length. The fluctuations in initiation length decrease as the pre-evaporation gas equivalence ratio increases for the unsteady cases. The results further suggest that the relationship between the evaporation layer thickness along the streamline and the corresponding theoretical initiation length can be used to identify an unsteady or steady ODW in cases with large droplets that evaporate behind an oblique shock wave or ODW under the effects of different initial droplet diameters.

We propose a linearized deterministic model for predicting coherent structures in the wake of a floating offshore wind turbine subject to platform motions. The model's motion-to-wake predictive capability is achieved through two building blocks: a motion-to-forcing (M2F) part and a forcing-to-wake (F2W) part. The M2F model provides a unified framework to parameterize the effects of arbitrary floating wind turbine motions as unsteady loads of a fixed actuator disk, requiring only the radial distribution of the aerodynamics force coefficient on the blade as input. The F2W model is derived based on a bi-global resolvent model obtained from the linearized Navier–Stokes equations, using the time-averaged wake of a fixed wind turbine as input. In addition to its capability of predicting sensitive frequency ranges, the model excels linear stability analysis by providing spatial modes of the wake response in a motion-specific and phase-resolved manner. The model successfully predicts the wake pulsing mode induced by surge, as well as the similarity and difference of the wake meandering modes caused by sway and yaw. Large-eddy simulations under different inflow turbulence intensities (TIs) and length scales are further conducted to analyse the wake meandering triggered by the simultaneous excitation of free-stream turbulence and sway motion. The results show distinct frequency signatures for the wake dynamics induced by ambient turbulence and sway motion. The inflow TI is found to have a stabilizing effect on the wake, reducing the motion-induced wake responses. Such a stabilizing effect is captured satisfactorily with the proposed model, provided that the effective viscosity is calibrated properly using the data from the fixed turbine wake under the corresponding turbulent inflow.

We design an open-loop active flow control for separated flows around a plunging circular cylinder based on resolvent analysis. The cylinder is plunging at a Strouhal number of 0.36 and a Reynolds number of 500. A linear time-periodic system for control is obtained by linearizing the non-inertial incompressible vorticity equation in the cylinder-fixed frame about a time-averaged base flow. Using the Lyapunouv–Floquet transformation, the linear time-periodic system is transformed into a similar linear time-invariant system, whose resolvent is analysed to obtain an optimal actuating Strouhal number of 0.1464 for the transformed linear system. Simulations show that the active control with tangential actuations is capable of reducing the lift fluctuation by up to 25.7 % when the flow is actuated near the predicted harmonic and subharmonic frequencies.