The effect of a series of thin, horizontal, low-permeability layers on convective motion from a distributed dense source along an upper boundary in an otherwise homogeneous, two-dimensional porous medium is considered. This set-up provides an idealised version of a relatively common form of heterogeneity in geological formations. The thickness and permeability of the thin layers are assumed to be small relative to the distance between them and the bulk permeability, respectively. As such, the layers can be parameterised by their impedance $\varOmega$ – a dimensionless ratio of the effective layer thickness and permeability – while the strength of convection is controlled by the dimensionless distance $H \gg 1$ between layers, which can also be interpreted as an effective Rayleigh number for the flow. The role of $\varOmega$ is explored with the aid of high-resolution numerical simulations, and simple analytical models are developed for the evolution of the mean concentration and the flux in the limits of small and large $\varOmega$. For intermediate values of $\varOmega$, the flow undergoes a transition from predominantly diffusive transfer across the layers to predominantly advective transfer, and the lateral scale of the flow can become very large. This transition is characterised and a simple model is developed.

Trailing-edge serrations inspired by owls are capable of reducing broadband noise. In this study, the wall-resolved large-eddy simulations (LES) are carried out on the flow over NACA-0012 airfoil with additional serrated trailing edges. The computations are conducted with the high-order flux reconstruction method on unstructured meshes. Three kinds of serrations with different lengths are studied and compared with the straight trailing-edge case, and all three types of serration achieved a certain degree of noise reduction. Presently, the medium-length serration achieves the best noise reduction effect. The maximum decrease of overall sound pressure level is approximately 2.4 dB, implying that the length of serration has a substantial impact on the noise reduction effect. The serration has no significant effect on the upstream turbulence statistics, but it changes the flow structure near the serration, such as inducing side vortex pairs attached to the serration edges. Moreover, dynamic mode decomposition shows that the pressure structures vary with the serration length. For the most unstable hydrodynamic wave, the spanwise coherence of the mode structure of pressure in the upstream boundary layer is weakened. In addition, serrations can redistribute the dipole sources on the surfaces of airfoil and serrations. The destructive interference is enhanced to some extent, which is favourable for noise reduction. In contrast with LES simulations, the pure dipole analysis shows that the longest serration case seems to be the best. Furthermore, a recently developed noise theory is used to evaluate the influence of serrations on the flow noise sources qualitatively and quantitatively. It is found that the serrations can mitigate noise source intensity near the serration edges but increase the source intensity in the near wake. The combined effect of serration on the dipole source and flow noise source determines the overall noise reduction effect. To conclude, destructive interference plays a primary role in suppressing noise radiation by serrated trailing edges, and the dual effect of flow noise sources should be considered in future serration designs. As the influence of turbulence structure will make it more difficult to find the optimal serration parameters, the position of high-fidelity simulation will become increasingly important.

In this paper we revive a special, less-common, variational principle in analytical mechanics (Hertz’ principle of least curvature) to develop a novel variational analogue of Euler's equations for the dynamics of an ideal fluid. The new variational formulation is fundamentally different from those formulations based on Hamilton's principle of least action. Using this new variational formulation, we generalize the century-old problem of the flow over a two-dimensional body; we developed a variational closure condition that is, unlike the Kutta condition, derived from first principles. The developed variational principle reduces to the classical Kutta–Zhukovsky condition in the special case of a sharp-edged airfoil, which challenges the accepted wisdom about the Kutta condition being a manifestation of viscous effects. Rather, we found that it represents conservation of momentum. Moreover, the developed variational principle provides, for the first time, a theoretical model for lift over smooth shapes without sharp edges where the Kutta condition is not applicable. We discuss how this fundamental divergence from current theory can explain discrepancies in computational studies and experiments with superfluids.

Motivated by an interest in inciting instabilities and mixing for heat transfer enhancement in ducts, flow in a channel with repeated wedge-shaped protrusions is considered for various blockage ratios (wedge height to duct height), pitch (distance between wedges) and wedge angles. The stability of the two-dimensional base flow and its dependence on the geometric parameters is elucidated through a global linear stability analysis. A linearly unstable two-dimensional mode was found, contrasting similar confined flow set-ups. However, the primary instability is a three-dimensional mode manifesting as counter-rotating streamwise vortices over the wedge tip. Analysis of the kinetic energy budget indicates a lift-up mechanism leading to instability, with the dominant energy gain of the global three-dimensional mode due to shear in the base flow. Structural sensitivity and receptivity of the instability to momentum forcing identifies the core of the instability and locations important for flow control. An endogeneity approach is used to show that the local perturbation pressure gradient component dominates the distribution of the local contribution to the growth rate of the linear global eigenmode in most cases considered, despite its net contribution being identically zero. Weakly nonlinear Stuart–Landau analysis reveals that the primary bifurcation is supercritical across all tested geometric parameter combinations. This is consistent with the finding of low linear transient growth amplifications at subcritical Reynolds numbers, being orders of magnitude lower than in similar channel flow set-ups.

We propose here a method to experimentally quantify unsteady leading-edge flow separation on aerofoils with finite thickness. The methodology relies on the computation of a leading-edge suction parameter based on measured values of the partial circulation around the leading edge and the stagnation point location. We validate the computation of the leading-edge suction parameter for both numerical and experimental data under steady and unsteady flow conditions. The leading-order approximation of the definition of the leading-edge suction parameter is proven to be sufficiently accurate for the application to thin aerofoils such as the NACA0009 without a priori knowledge of the stagnation point location. The higher-order terms including the stagnation point location are required to reliably compute the leading-edge suction parameter on thicker aerofoils such as the NACA0015. The computation of the leading-edge suction parameter from inviscid flow theory does not assume the Kutta condition to be valid at the trailing edge which allows us to compute its value for separated flows. The relation between the leading-edge suction parameter and the evolution of the shear layer height is studied in two different unsteady flow conditions, a fixed aerofoil in a fluctuating free-stream velocity and a pitching aerofoil in a steady free stream. We demonstrate here that the instantaneous value of the leading-edge suction parameter based on the partial circulation around the leading edge is unambiguously defined for a given flow field and can serve as a directly quantitative measure of the degree of unsteady flow separation at the leading edge.

Instability of collapsible tubes is studied theoretically and experimentally in many papers in the context of biological applications. Up to the present day, only Newtonian fluid flows in elastic tubes have been studied. However, there are circumstances when blood, bile and other biological fluids show essentially non-Newtonian behaviour. In this paper, we re-investigate theoretically axisymmetric stability of elastic tubes conveying power-law fluids. It is shown that for the power-law index $n=1$, i.e. for the Newtonian case, axisymmetric disturbances in infinite-length tubes are damped, which is in accordance with experimental and theoretical observations, where the oscillations always involve non-axisymmetric motion of the tube walls. However, for $n<0.611$, the axisymmetric disturbances can be growing, which predicts a new type of instability of elastic tubes conveying pseudoplastic (shear-thinning) fluids. For $n<1/3$, local instability of axisymmetric perturbations becomes absolute in infinite tubes, while finite-length tubes become globally unstable. The effects of the axial tension, elastic tube length and, if present, lengths of inlet and outlet rigid tubes on the stability of finite-length tubes are analysed.

A new lattice Boltzmann model (LBM) for chemically reactive mixtures is presented. The approach capitalizes on the recently introduced thermodynamically consistent LBM for multicomponent mixtures of ideal gases. Similar to the non-reactive case, the present LBM features Stefan–Maxwell diffusion of chemical species and a fully on-lattice mean-field realization of the momentum and energy of the flow. Besides introducing the reaction mechanism into the kinetic equations for the species, the proposed LBM also features a new realization of the compressible flow by using a concept of extended equilibrium on a standard lattice in three dimensions. The full thermodynamic consistency of the original non-reactive multicomponent LBM enables us to extend the temperature dynamics to the reactive mixtures by merely including the enthalpy of formation in addition to the sensible energy considered previously. Furthermore, we describe in detail the boundary conditions to be used for reactive flows of practical interest. The model is validated against a direct numerical simulation of various burning regimes of a hydrogen/air mixture in a microchannel, in two and three dimensions. Excellent comparison in these demanding benchmarks indicates that the proposed LBM can be a valuable and universal model for complex reactive flows.

A turbulent drag-reduction method employing synthetic jet sheets in a turbulent channel flow is investigated by direct numerical simulations. The jet sheets are wall-parallel and produced by periodic blowing and suction from pairs of thin slots aligned with the main streamwise flow. By varying the slot height and the jet-sheet angle with respect to the spanwise direction, drag-reduction margins between $10\,\%$ and $30\,\%$ are obtained for jet-sheet angles between $45 ^{\circ }$ and $75 ^{\circ }$, while a drag increase of almost 100 % is computed when the jet sheets are spanwise-oriented. When global skin-friction drag reduction occurs, the wall-shear stress near the jet-sheet exits increases during suction and decreases during blowing, while the velocity fluctuations weaken during suction and intensify during blowing. The global drag-reduction effect is produced by a finite counter flow induced by the nonlinear interaction between the jet-sheet flow and the main flow, although the turbulent intensity and Reynolds shear stresses increase. The power spent to generate the jet sheets is computed by modelling numerically the actuator underneath the channel flow as a piston oscillating sinusoidally along the spanwise direction in a round-shaped cavity from which the fluid is released into the channel through the cavity exits. A power balance leads to the computation of the efficiency of the actuator system, quantifying the portion of the piston power that is lost as internal power fluxes and heat transfer through the cavity walls. For the tested configurations, the power consumed by the piston to generate the jet sheets is larger than the power saved thanks to the drag reduction.

When viscous fluid in a corner is disturbed, eddies can form in the absence of inertia. Examples of flow configurations in which this motion occurs include flow through an abrupt contraction and over a cavity. Six decades ago, Moffatt (J. Fluid Mech., vol. 18, 1964, pp. 1–18) calculated the slow viscous flow of Newtonian fluids in sharp corners, detailing his eponymous ‘Moffatt eddies’. In this study we examine corner flows of viscoplastic materials, a class of non-Newtonian fluids which exhibit solid-like behaviour for stresses below a yield stress. Specifically, we consider a Bingham fluid, for which the material is perfectly rigid at stresses below the yield stress. While a static unyielded plug forms at the tip of the corner, eddies analogous to those found by Moffatt can also form. We examine these viscoplastic eddies numerically, by computing finite element solutions using the augmented-Lagrangian method, and analytically, by employing a viscoplastic boundary layer formulation and scaling arguments. We measure the depth of the static plug as a function of the Bingham number (dimensionless yield stress), show that the process of a new eddy forming as the Bingham number is decreased is driven by the pressure in the yielded fluid adjacent to the static plug, and provide a heuristic argument for the critical Bingham number at which this occurs.

The Richtmyer–Meshkov instability of heavy/light single-mode (SM), trapezoid (TR) and sawtooth (ST) interfaces is studied experimentally by considering the reshock. The TR and ST interfaces can be expanded into Fourier series with a dominant fundamental mode and more high-order modes, recognized as quasi-single-mode ones. In experiments, the distorted interfaces at the time of first reshock arrival develop in the weakly nonlinear stage, ensuring an approximate single-scale function of evolving interface. The results show an evident memory of initial interface shapes: the bubbles and spikes of ST interface after reshock mainly develop in the streamwise direction with sharp heads, while the counterparts of TR interface tend to grow in the spanwise direction. The influences of high-order modes are amplified by the reshock, resulting in significant interface shape dependence of mixing width growths. The amplitude superposition of major odd-order modes promotes the growth rates of mixing widths for the SM and ST cases, different from the TR one. The ST interface has larger mixing width growth rates in comparison with the SM interface, since high-order modes play a great role in promoting the increase of ST amplitudes, while the TR interface has a relatively small one. The linear and nonlinear mixing width growths of SM, TR and ST interfaces before and after reshock are further analysed theoretically, indicating that the fundamental mode still has a predominant influence on the interface evolution after reshock, and the growth behaviours exhibit strong similarities to those for the singly shocked cases.

In the limit of large magnetic Reynolds numbers, it is shown that a smooth differential rotation can lead to fast dynamo action, provided that the electrical conductivity or magnetic permeability is anisotropic. If the shear is infinite, for example between two rotating solid bodies, the anisotropic dynamo becomes furious, meaning that the magnetic growth rate increases toward infinity with an increasing magnetic Reynolds number.

Over-the-rotor liner exhibits the potential to further attenuate turbofan noise, but the physics involved remain to be explored. In this paper, a three-dimensional coupled singularity method is proposed to investigate the flow-acoustic coupling effects of axially overlapping annular rotor and finite-length liner in subsonic flow. The formulation adopts the orthogonal basis expansion of the generated disturbances in terms of the hard-walled duct modes. The sound scatterings at the rotor and the liner are then characterized, respectively, by the underdetermined dipole and monopole distributions. We derive a simultaneous solution to the coupled unsteady rotor and liner responses, which ensures that the resultant perturbed field satisfies both the impermeable boundary condition on the blade surfaces and the impedance boundary condition on the lined wall. The effect of a perforated porous-material liner on the wake–rotor interaction tones is investigated. The analysis reveals that for the sound field of varying mode and frequency characteristics, moving the inlet liner to the over-the-rotor location generally leads to limited loss or even an increase of upstream sound absorption, along with additional acoustic benefits in the aft duct. The flow-acoustic coupling between the axially overlapping rotor and liner is shown to alleviate significantly the unsteady blade loading and meanwhile intensify the fluid particle oscillation through the acoustically treated wall. Sound source reduction and sound dissipation enhancement are thus identified as the governing noise attenuation mechanisms. Finally, we extend the analysis to provide insights into the effectiveness of over-the-rotor acoustic treatment with shortened axial length.

The modulations of high/low-speed large-scale motions (H/L-SMs) on the turbulent/non-turbulent interface (TNTI) and turbulent entrainment are investigated in turbulent boundary layers via both experimental and numerical studies. The spanwise locations of large-scale motions can be locked by the spanwise heterogeneity, so the boundary layers over such a configuration are investigated first as an instructive case. In the engulfment process, it is found that irrotational ‘bubbles’ near the TNTI are more likely to originate from engulfment, while bubbles far from the TNTI could be produced by the local turbulence itself. Additionally, H-SMs are found to enhance the engulfment by the sweep flow. In the nibbling process, a competition relationship is observed: L-SMs induce stronger instantaneous ‘nibbling’ events by transporting more fluids towards the TNTI, while the H-SMs induced a more distorted TNTI. Consequently, the integral nibbling flux is greater above H-SMs. Furthermore, the explored mechanisms are verified to be insensitive to the wall shapes such as smooth and homogeneous roughness walls, which demonstrates that these modulations are universal for turbulent boundary layers. Finally, a conceptual modulation model is proposed to illustrate the entrainment process above the large-scale motions.