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The flow of liquids through paper is challenging to model due to the complexity and disordered layout of the fibre matrix. The expanding use and capability of microfluidic paper-based analytical devices (μPADs) and their requirement for precision has increased the need to accurately predict the flow of liquids through paper. Many studies have developed models and revealed some of the physical mechanisms responsible for the flow behaviour, but we still lack a complete understanding, particularly in relation to how the fluid fills the various voids with a wide range of shapes and sizes in the fibre matrix of paper. In the featured article, Chang et al. (J. Fluid Mech., vol. 845, 2018, 36-50) used a combined experimental and theoretical approach to uncover the importance of the liquid filling the intra-fibre pores, showed that this results in deviation from the flow behaviour predicted by the Lucas--Washburn equation and developed a model which accounts for this effect. [ABSTRACT FROM AUTHOR]

We present a combined experimental and theoretical investigation of the dynamics of water imbibition through paper with swelling. The Washburn equation has been widely used to describe the dynamics of the liquid absorption in paper, but its prediction of liquid imbibition speed has been reported to be inaccurate. Our recent study (Chang et al., J. Fluid Mech., vol. 845, 2018, pp. 36–50) demonstrated that the internal cavity of cellulose fibres composing the paper is partially responsible for the limited accuracy of the Washburn equation based on oil imbibition experiments. Here we extend the investigation to water absorption through paper with swelling. We demonstrate that the swelling of the cellulose fibre network in addition to the internal voids of the cellulose fibres crucially affects the imbibition dynamics. Based on the microscopic observation that paper swelling is caused by the expansion of inter-fibre space, we suggest a mathematical model for water imbibition which considers both intra-fibre voids and swelling. By introducing parameters that characterize the swelling speed and volume of paper, our model markedly improves prediction of the water imbibition speed. The results provide not only a theoretical background for designing paper-based microfluidic systems, but also new insights into capillary flow through expandable porous media. [ABSTRACT FROM AUTHOR]

We present a combined experimental and theoretical investigation of the dynamics of liquid imbibition through paper. The Washburn equation is widely used to describe the dynamics of capillary flow through paper, but this classical model has limited accuracy, which often makes it difficult to use in developing analytic systems such as paper-based microfluidic devices. We here report that the internal cavity of the cellulose fibres composing paper is significantly responsible for the limited accuracy of the Washburn equation. Our experiments demonstrated that liquid can be absorbed in the internal cavity of the cellulose fibres as well as in the inter-fibre pores formed by the fibre network. We developed a mathematical model for liquid imbibition by considering the flow through the intra-fibre pores based on experimental measurements of the intra-structure of cellulose fibres. The model markedly improves the prediction of the liquid absorption length, compared with the results of the Washburn equation, thus revealing the physics behind the limits of the Washburn equation. This study suggests that the accurate description of capillary imbibition through paper require parameters characterizing the internal pores of the cellulose fibres comprising the paper. Our results not only provide a new insight into porous media flows with different sized pores, but also provide a theoretical background for flow control in paper-based microfluidic systems. [ABSTRACT FROM AUTHOR]

Maas (J. Fluid Mech., vol. 684, 2011, pp. 5–24) showed that, for an oscillating two-dimensional barotropic tide flowing over sub-critical topography of compact support, some topographic forms existed that produced non-radiating baroclinic disturbances. The problem is related to 'stealth' and 'cloaking' problems. Here Maas's result is derived using a simpler approach, not involving complicated mappings, but formally restricted to perturbation topography. Wider results come from the discussion of nearly compact support topographic disturbances provided by Schwartz functions with weak high-wavenumber radiation and by exploiting both a known functional equation formulation and Fourier methods. The problem is extended to disturbances on uniform slopes. A variety of non-radiating topographies can be found, although they are mathematically delicate and unlikely to be found in nature. Topography with weak radiation at high wavenumber is a much wider class of structures. Application of these solutions would lie with the ability to estimate dissipation over and near the topography from motions observed at a distance. [ABSTRACT FROM AUTHOR]

A distinguishing feature of the bi-stable wake is that the wake persists in either of two preferred states for a sufficiently long time. Aiming to understand the persistence mechanism, this paper numerically investigates the airwake characteristics of the Chalmers ship model (CSM) using large eddy simulation with a wall-adapting local-eddy viscosity model and is complemented by experimental testings for validations. There are two cases of interest: (i) the baseline CSM with a sharp-edged superstructure front that induces massive boundary layer separation; (ii) the front-rounded (FR) CSM with suppressed flow separation. During a characteristic time ($t^*$) of 1142 (26.5 s), the baseline case has a frequently switching wake, whereas the FR wake maintains a stable asymmetric structure with only one switch attempt. To understand the different wake behaviours, the study starts by analysing wake flow structures, vortex cores and the wake dynamics, followed by investigating the instantaneous flow physics. Results suggest that the baseline wake has a weak bi-stable pattern, whereas the FR wake behaves similarly to a reflectional symmetry breaking state of a potential bi-stable wake. The wake switching is found to be driven by the tilting of (vertical-oriented) $z$ -vorticity sheets from either side of the base toward the centre. This tilting behaviour is subjected to the high-magnitude vorticity that sheds from the upstream flow separation at the front sharp edges. With the sharp edges rounded in the FR case, the upstream vorticity is mitigated and the tilting effect is significantly reduced, leading to a more stable wake structure. The reasoning provided in the paper potentially explains the persistence mechanism of the bi-stable wake. [ABSTRACT FROM AUTHOR]

Growth of a fluid-infused patch on a thin porous layer, e.g. on a piece of paper or cloth, is related to the transmission of virus particles through exhaled droplets and aerosols. We present a theoretical model to describe how a wet patch develops gradually through imbibition, once a sessile droplet attaches at a permeable surface and drains gradually into a thin porous layer. Two limiting cases are considered based on different assumptions on the motion of the contact line during the coupled process of drop drainage and patch growth: (i) the apparent contact angle remains unchanged, so the radius of a sessile droplet decreases with time; and (ii) the location of the contact line remains pinned, so the contact angle decreases as time progresses. The model leads to evolution pathways for both the droplet and the fluid film within the porous layer, without introducing arbitrary fitting parameters. Potential implications of the model and its solutions are also discussed briefly in the context of the outspread of COVID-19, employing physical parameters for exhaled droplets, paper and cloth. [ABSTRACT FROM AUTHOR]

This paper is concerned with the optimal upper bound on mean quantities (torque, dissipation and the Nusselt number) obtained in the framework of the background method for the Taylor-Couette flow with a stationary outer cylinder. Along the way, we perform the energy stability analysis of the laminar flow, and demonstrate that below radius ratio 0.0556, the marginally stable perturbations are not the axisymmetric Taylor vortices but rather a fully three-dimensional flow. The main result of the paper is an analytical expression of the optimal bound as a function of the radius ratio. To obtain this bound, we begin by deriving a suboptimal analytical bound using analysis techniques. We use a definition of the background flow with two boundary layers, whose relative thicknesses are optimized to obtain the bound. In the limit of high Reynolds number, the dependence of this suboptimal bound on the radius ratio (the geometrical scaling) turns out to be the same as that of numerically computed optimal bounds in three different cases: (1) the perturbed flow only satisfies the homogeneous boundary conditions but need not be incompressible; (2) the perturbed flow is three-dimensional and incompressible; (3) the perturbed flow is two-dimensional and incompressible. We compare the geometrical scaling with the observations from the turbulent Taylor-Couette flow, and find that the analytical result indeed agrees well with the available direct numerical simulations data. In this paper, we also dismiss the applicability of the background method to certain flow problems and therefore establish the limitation of this method. [ABSTRACT FROM AUTHOR]

This paper introduces a new operator relevant to input–output analysis of flows in a statistically steady regime far from the steady base flow: the mean resolvent ${{\boldsymbol{\mathsf{R}}}}_0$. It is defined as the operator predicting, in the frequency domain, the mean linear response to forcing of the time-varying base flow. As such, it provides the statistically optimal linear time-invariant approximation of the input–output dynamics, which may be useful, for instance, in flow control applications. Theory is developed for the periodic case. The poles of the operator are shown to correspond to the Floquet exponents of the system, including purely imaginary poles at multiples of the fundamental frequency. In general, evaluating mean transfer functions from data requires averaging the response to many realizations of the same input. However, in the specific case of harmonic forcings, we show that the mean transfer functions may be identified without averaging: an observation referred to as 'dynamic linearity' in the literature (Dahan et al. , J. Fluid Mech. , vol. 704, 2012, pp. 360–387). For incompressible flows in the weakly unsteady limit, i.e. when amplification of perturbations by the unsteady part of the periodic Jacobian is small compared to amplification by the mean Jacobian, the mean resolvent ${{\boldsymbol{\mathsf{R}}}}_0$ is well-approximated by the well-known resolvent operator about the mean flow. Although the theory presented in this paper extends only to quasi-periodic flows, the definition of ${{\boldsymbol{\mathsf{R}}}}_0$ remains meaningful for flows with continuous or mixed spectra, including turbulent flows. Numerical evidence supports the close connection between the two resolvent operators in quasi-periodic, chaotic and stochastic two-dimensional incompressible flows. [ABSTRACT FROM AUTHOR]

The present paper numerically investigates the fluid dynamics associated with the flow over an elastically mounted circular cylinder at a Reynolds number of 500. A slit normal to the flow direction is placed at the cylinder's centre. The study covers the large parametric set of calculations for the combined mass-damping ratio $m^{*}\zeta = 0.2$ , including the slit offset for six different offset angles ($-30^\circ \leq \alpha \leq +30^\circ$) measured from the vertical axis at the centre point of the cylinder and the effect of slit widths ($0.1 \leq s/D \leq 0.3$) on the aerodynamic loading, vibration response and associated flow characteristics. Furthermore, a wide range of reduced velocities ($3\leq U_r \leq 7$) are examined for the complete closure of studying the effect on the vortex-induced vibration response. The results demonstrate that adding the normal slit increases the periodic suction-blowing phenomena, strengthening the vortex shedding. The results suggest that the normal slit can suppress or increase vortex-induced vibration depending on the slit-offset angle. Placing it toward the front stagnation point results in the increased oscillation amplitude (with a wider wake behind the cylinder) while shifting it toward the rear stagnation point diminishes the cylinder's oscillations. The paper reveals that this dual behaviour of the normal slit (based on its offset placement) is closely related to the phase difference between the lift force and the oscillation amplitude. Various vortex-shedding patterns associated with the different slit-offset angles are duly reported in the paper. Furthermore, a magnet is attached to the slit cylinder, and its effect on the energy harvesting capability via a coil-magnet arrangement is explored in detail for a wide range of reduced velocities. [ABSTRACT FROM AUTHOR]

The swinging motion of the eigenmodes of a free inviscid drop has been known for nearly a century. Yet, as the drop sits on a solid substrate, getting flattened by gravity, analytical solutions waver due to the non-spherical base state and the dynamics of the three-phase contact line. The recent paper by Zhang et al. (J. Fluid Mech., vol. 962, 2023, A10) investigated the effect of gravity on the harmonic modes of sessile droplets for free and pinned contact line conditions. An effective boundary element method has been used to solve both axisymmetric and non-axisymmetric modes for a variety of Bond numbers and static contact angles, also revising on the way a debated capillary instability. [ABSTRACT FROM AUTHOR]

The article presents information on the changes that will be made to the journal.

This paper describes the mechanism underpinning modal staging behaviour in screeching jets. An upstream-propagating subsonic guided-jet mode is shown to be active in all stages of screech. Axial variation of shock-cell spacing manifests in the spectral domain as a series of suboptimal peaks. It is demonstrated that the guided-jet mode may be energized by interactions of the Kelvin–Helmholtz wavepacket with not only the primary shock wavenumber peak, but also suboptimal peaks; interaction with suboptimals is shown to be responsible for closing the resonance loop in multiple stages of jet screech. A consideration of the full spectral representation of the shocks reconciles several of the classical models and results for jet screech that had heretofore been paradoxical. It is demonstrated that there are multiple standing waves present in the near field of screeching jets, corresponding to the superposition of the various waves active in these jets. Multimodal behaviour is explored for jets in a range of conditions, demonstrating that multiple peaks in the frequency spectra can be due to either changes in which peak of the shock spectra the Kelvin–Helmholtz wavepacket is interacting with, or a change in azimuthal mode, or both. The absence of modal staging in high-aspect-ratio non-axisymmetric jets is also explained in the context of the aforementioned mechanism. The paper closes with a new proposed theory for frequency selection in screeching jets, based on the observation that these triadic interactions appear to underpin selection of the guided-jet mode wavelength in all measured cases. [ABSTRACT FROM AUTHOR]

The interaction between ingested turbulence and rotating blades is a key source of broadband noise in engineering applications. In this paper, a far-field noise model accounting for source correlation across the span of the blade and between blades is developed and applied to the study of homogeneous isotropic turbulence ingestion by a model cooling fan, wind turbine and aircraft propeller. The widely used theory of Amiet is revisited and it is shown that previous works produce conflicting results when attempting to account for blade-to-blade correlation. Central to the model is the calculation of the time between blade chops of the same turbulent eddy as heard by the observer. In this paper it is shown that, when derived correctly, Amiet's theory accounts for correlated sources between blades and, thus, can predict haystacking tones. Comparisons with the new rotational formulation and with experimental data enable us to show that Amiet's theory can be used to accurately predict turbulence ingestion noise from open rotors. In particular, it is found that the infinite-span assumption in strip theory and the neglect of correlation effects across the span do not undermine the accuracy of this theory. This is of great importance because, unlike Amiet's theory, models which treat rotational effects and source correlation exactly are expensive to evaluate routinely at high frequencies due to the slow convergence of infinite series with Bessel functions. [ABSTRACT FROM AUTHOR]

The presence of a solid boundary can cause a substantial increase in added mass due to a solid body movement in the fluid. If the body is very close to the boundary, the added mass increases at an even greater rate. The added mass can be of considerable importance in many dams and hydropower, water/ocean, civil and mechanical engineering problems; furthermore, it has an important effect on the dynamics of the vibrating body in the fluid. The principal aim of this paper is to define a novel model to properly evaluate the near-bottom effects of the added mass and to investigate the instantaneous pressure field due to a body movement that changes the thickness of a compressible thin fluid film close to a solid boundary. The body movement can be due to the application of an external force according to Newton's law. This phenomenon is studied theoretically in this paper, and a hydrodynamic model able to compute the instantaneous pressure field in the thin fluid film is drawn out. The fluid film thickness variation, producing compression and decompression waves, tends to reduce the mean body displacement due to external forces, but it generates both high-frequency fluctuations in body force and in body displacements. For the first time, this novel study provides the near-bottom added mass and justifies the strong body accelerations measured in the laboratory experiments that have not been evidenced in the theoretical studies in the known literature. [ABSTRACT FROM AUTHOR]

We show that in the linear approximation there are three classes of reflectionless wave propagation on a surface of shallow water in the channel with spatially varying depth, width and current speed. Two of these classes have been described in our previous paper (Churilov & Stepanyants, J. Fluid Mech., vol. 931, 2022, A15), and the third one was discovered recently and is described here. The general analysis of the problem shows that, within the approach used in both of our papers, these three classes apparently exhaust all possible cases of exact solutions of the problem considered. We show that the reflectionless flow can be global for certain conditions, i.e. it can exist on the entire x-axis. There are also reflectionless flows which exist only on limited intervals of the x-axis. [ABSTRACT FROM AUTHOR]

Viscous flow around two spherical macroscopic cavities (or void spaces) in a granular material, which is exposed to an otherwise uniform flow at infinity, is investigated. The flow field is obtained analytically by solving the Stokes equation inside and the Darcy–Brinkman equation outside of the cavities, where continuity of the velocity and that of the stress are assumed on the boundary. In our previous complementary paper (Sano, Karmakar & Sekhar, J. Fluid Mech. , vol. 931, 2022, A20), we obtain that two cavities of equal size in a tandem position are more prone to collapse for a shorter centre-to-centre distance with low permeability. In the present study, the asymptotic analysis of the interaction of two spherical cavities of different sizes with arbitrary configuration is presented. Particular attention is paid to the configuration dependence of two cavities of equal radius. The velocity field and the volume flux into respective cavities are calculated, which reveal that two cavities with orientation less than a certain critical angle are given a larger volume flux and are more prone to collapse. The present results are applicable to predicting the behaviour in a fixed-bed regime of a solid–gas transport system, microscale waterway formation in a granular material, onset of landslides, collapse of cliffs and river banks, etc. [ABSTRACT FROM AUTHOR]

In this paper, we study the local receptivity of the inviscid Mack modes in hypersonic boundary layers induced by the interaction between a surface heating or cooling source (HCS) and a freestream acoustic wave. The asymptotic analysis reveals that among the three distinguished layers, i.e. the main, wall and Stokes layers, the leading-order receptivity is attributed to the interaction of the HCS-induced mean-flow distortion and the acoustic signature in the wall layer; the second-order contribution appears in the Stokes layer; the third-order contribution appears in both the main and wall layers. Interestingly, at a moderate Reynolds number, the third-order contribution to the receptivity efficiency may be quantitatively greater than the second-order one, but this does not lead to breakdown of this asymptotic theory. Assuming the HCS intensity to be sufficiently weak, the asymptotic predictions are made for four representative cases involving different Mach numbers and wall temperatures, which are compared with the results obtained by the finite-Reynolds-number theory based on either the extended compressible Orr–Sommerfeld equations or the harmonic linearised Navier–Stokes (HLNS) calculations. Taking into account the first three orders of the receptivity efficiency, the asymptotic predictions are confirmed to be sufficiently accurate even when the Reynolds number is a few thousands, and the agreement with the finite-Reynolds-number calculations is better when the wall temperature of the base flow approaches the adiabatic wall temperature. The HLNS calculations are also conducted for moderate HCS intensities. It is found that the nonlinearity does not affect the receptivity coefficient much even when the temperature distortion of the HCS reaches $80\,\%$ of the temperature at the wall. [ABSTRACT FROM AUTHOR]

Three-dimensional steady-state Arnold–Beltrami–Childress (ABC) flow has a chaotic Lagrangian structure, and also satisfies the Navier–Stokes (NS) equations with an external force per unit mass. It is well known that, although trajectories of a chaotic system have sensitive dependence on initial conditions, i.e. the famous 'butterfly effect', their statistical properties are often insensitive to small disturbances. This kind of chaos (such as governed by the Lorenz equations) is called normal-chaos. However, a new concept, i.e. ultra-chaos, has been reported recently, whose statistics are unstable to tiny disturbances. Thus, ultra-chaos represents higher disorder than normal chaos. In this paper, we illustrate that ultra-chaos widely exists in Lagrangian trajectories of fluid particles in steady-state ABC flow. Moreover, solving the NS equation when $Re=50$ with the ABC flow plus a very small disturbance as the initial condition, it is found that trajectories of nearly all fluid particles become ultra-chaotic when the transition from laminar to turbulence occurs. These numerical experiments and facts highly suggest that ultra-chaos should have a relationship with turbulence. This paper identifies differences between ultra-chaos and sensitivity of statistics to parameters. Possible relationships between ultra-chaos and the Poincaré section, ultra-chaos and ergodicity/non-ergodicity, etc., are discussed. The concept of ultra-chaos opens a new perspective of chaos, the Poincaré section, ergodicity/non-ergodicity, turbulence and their inter-relationships. [ABSTRACT FROM AUTHOR]

We investigate experimentally and theoretically the stability of a shear-thickening suspension flowing down an inclined plane. In a previous paper (Darbois Texier et al. , Commun. Phys. , vol. 3, 2020), we have shown that for particle volume fractions $\phi$ above the discontinuous shear-thickening fraction $\phi _{DST}$ , long surface waves grow spontaneously at a flow Reynolds number much below 1. This motivated a simplified analysis based on a purely inertialess mechanism, called the 'Oobleck waves' mechanism, which couples the negatively sloped rheology of the suspension with the free-surface deflection and captures well the experimental instability threshold and the wave speed, for $\phi >\phi _{DST}$. However, neglecting inertia does not allow us to describe the inertial Kapitza regime observed for $\phi , nor does it allow us to discriminate between Oobleck waves and other inertial instabilities expected above $\phi _{DST}$. This paper fills this gap by extending our previous analysis, based on a depth-averaged approach and the Wyart–Cates constitutive shear-thickening rheology, to account for inertia. The extended analysis recovers quantitatively the experimental instability threshold in the Kapitza regime, below $\phi _{DST}$ , and in the Oobleck waves regime, above $\phi _{DST}$. By providing additional measurements of the wave growth rate and investigating theoretically the effect of a strain delay in the rheology, it also confirms that the instability observed above $\phi _{DST}$ stems from the non-inertial Oobleck wave mechanism, which is specific to free-surface flows and dominates modes of inertial origin. These results emphasize the variety of instability mechanisms for shear-thickening suspensions and might be relevant to free-surface flows of other complex fluids displaying velocity-weakening rheology. [ABSTRACT FROM AUTHOR]

When studying instability of weakly non-parallel flows, it is often desirable to convert temporal growth rates of unstable modes, which can readily be computed, to physically more relevant spatial growth rates. This has been performed using the well-known Gaster's transformation for primary instability and Herbert's transformation for the secondary instability of a saturated primary mode. The issue of temporal–spatial transformation is revisited in the present paper to clarify/rectify the ambiguity/misunderstanding that appears to exist in the literature. A temporal mode and its spatial counterpart may be related by sharing either the real frequency or wavenumber, and the respective transformations between their growth rates are obtained by a simpler consistent derivation than the original one. These transformations, which consist of first- and second-order versions, are valid under conditions less restrictive than those for Gaster's and Herbert's transformations, and reduce to the latter under additional conditions, which are not always satisfied in practice. The transformations are applied to inviscid Rayleigh instability of a mixing layer and a jet, secondary instability of a streaky flow as well as general detuned secondary instability (including subharmonic and fundamental resonances) of primary Mack modes in a supersonic boundary layer. Comparison of the transformed growth rates with the directly calculated spatial growth rates shows that the transformations derived in this paper outperform Gaster's and Herbert's transformations consistently. The first-order transformation is accurate when the growth rates are small or moderate, while the second-order transformations are sufficiently accurate across the entire instability bands, and thus stand as a useful tool for obtaining spatial instability characteristics via temporal stability analysis. [ABSTRACT FROM AUTHOR]

This paper revisits the study by Bailey et al. (J. Fluid Mech., vol. 615, 2008, pp. 121-138), adopting a higher-fidelity calibration approach to reveal subtle flow variations with Reynolds numbers that were not discernible previously. The paper aims therefore to provide insights into the characteristics of azimuthal and streamwise pipe flow structures adopting two-point joint statistics and spectral analysis for shear Reynolds numbers in the range 2 × 10³ = Ret = 16 × 10³, where Ret is based on the wall friction velocity ut, the pipe radius R, and the fluid kinematic viscosity?. The streamwise velocity fluctuations were measured at four wall-normal locations, 0.1 = x2/R = 0.7, covering the logarithmic and core regions of fully developed turbulent pipe flow based on 35-41 azimuthal probe separations using, simultaneously, two single hot-wire probes. A unique in situ calibration approach for both probes was adopted where a potential flow was insured, resulting in consistent and precise pipe flow data. The azimuthal velocity correlation, the cross-power spectral density and the coherence function of the streamwise velocity fluctuations are discussed, revealing a clear dependence of the azimuthal scales of the large and very large flow motions on the wall-normal location, the azimuthal separation, the streamwise wavenumber and the Reynolds number. Along the logarithmic region, a linear growth of the azimuthal scales of the large- and very-large-scale structures was observed; however, they do scale nonlinearly and reach their maximum sizes in the core region, i.e. near the centreline of the pipe. Additionally, the streamwise very-large-and large-scale motions were evaluated using the premultiplied energy spectra, showing wavelengths ?18R and ?3R for Ret = 16 × 10³ at half of the pipe radius, respectively. [ABSTRACT FROM AUTHOR]

This paper studies the instability of two-dimensional magnetohydrodynamic systems on a sphere using analytical methods. The underlying flow consists of a zonal differential rotation and a toroidal magnetic field is present. Semicircle rules that prescribe the possible domain of the wave velocity in the complex plane for general flow and field profiles are derived. The paper then sets out an analytical study of the 'clamshell instability', which features field lines on the two hemispheres tilting in opposite directions (Cally, Sol. Phys. , vol. 199, 2001, pp. 231–249). An asymptotic solution for the instability problem is derived for the limit of weak shear of the zonal flow, via the method of matched asymptotic expansions. It is shown that when the zonal flow is solid body rotation, there exists a neutral mode that tilts the magnetic field lines, referred to as the 'tilting mode'. A weak shear of the zonal flow excites the critical layer of the tilting mode, which reverses the tilting direction to form the clamshell pattern and induces the instability. The asymptotic solution provides insights into properties of the instability for a range of flow and field profiles. A remarkable feature is that the magnetic field affects the instability only through its local behaviour in the critical layer. [ABSTRACT FROM AUTHOR]

This study is an attempt at solving steady-state triple-deck equations using the method of Bos & Ruban (Phil. Trans. R. Soc. Lond. A, vol. 358, issue 1777, 2000, pp. 3063–3073) for supersonic flow past a compression corner. This was motivated by the fact that in their above paper, they show solutions for scale angles up to 8, the highest obtained so far in the literature. However, we encountered a stationary wave-packet at the corner for scale angles 1.82 and 1.96, depending on the values of stretching factors. Our solutions are then compared with the steady-state solutions produced using the method of Logue, Gajjar & Ruban (Phil. Trans. R. Soc. A, vol. 372, issue 2020, 2014, 20130342), which do not show such wave-packets. These wave-packets do not appear to be the result of flow instability, as flow instabilities should only appear with unsteady equations (Cassel, Ruban & Walker, J. Fluid Mech. , vol. 300, 1995, pp. 265–285). It is therefore suggested that the method of Bos & Ruban (Phil. Trans. R. Soc. Lond. A, vol. 358, issue 1777, 2000, pp. 3063–3073) produces these spurious wave-packets as a consequence of their numerical method. This has important implications in the interpretation of triple-deck solutions. [ABSTRACT FROM AUTHOR]

This paper presents a systematic analysis of direct and adjoint problems for sound propagation with flow. Two scalar propagation operators are considered: the linearised potential equation from Goldstein, and Pierce's equation based on a high-frequency approximation. For both models, the analysis involves compressible base flows, volume sources and surfaces that can be vibrating and/or acoustically lined (using the Myers impedance condition), as well as far-field radiation boundaries. For both models, the direct problems are fully described and adjoint problems are formulated to define tailored Green's functions. These Green's functions are devised to provide an explicit link between the direct problem solutions and the source terms. These adjoint problems and tailored Green's functions are particularly useful and efficient for source localisation problems, or when stochastic distributed sources are involved. The present analysis yields a number of new results, including the adjoint Myers condition for the linearised potential equation, as well as the formulation of the direct and adjoint Myers condition for Pierce's equation. It is also shown how the adjoint problems can be recast in forms that are readily solved using existing simulation tools for the direct problems. Results presented in this paper are obtained using a high-order finite element method. Several test cases serve as validation for the approach using tailored Green's functions. They also illustrate the relative benefits of the two propagation operators. [ABSTRACT FROM AUTHOR]

This paper describes, from a theoretical point of view, the appearance and characteristics of granular roll waves in chute flow, and the maximal size these waves can attain for a given influx of material into the system. Granular roll waves are steady travelling wave solutions of the generalized Saint-Venant equations for flowing granular matter, appearing when the Froude number $Fr$ of the incoming flow exceeds a critical value, $Fr>Fr_{cr}$. We focus upon the phase space of the corresponding dynamical system, where the roll waves take the form of a stable limit cycle around an unstable fixed point; this limit cycle gives precise information on the size and periodicity of the roll wave. It is found that, for any given value of $Fr$ , the limit cycle cannot become arbitrarily large because it is constrained by a homoclinic loop in phase space. Roll waves of larger amplitude can be generated by increasing the Froude number $Fr$. [ABSTRACT FROM AUTHOR]

An experiment was performed using stereo particle image velocimetry (SPIV) in the Laboratoire de Mécanique des Fluides de Lille boundary layer facility to determine all the derivative moments needed to estimate the average dissipation rate of the turbulence kinetic energy $\epsilon = 2 \nu \langle {\mathsf{s}}_{ij}{\mathsf{s}}_{ij} \rangle$ , where ${\mathsf{s}}_{ij}$ is the fluctuating strain rate and $\langle ~\rangle$ denotes ensemble averages. Also measured were all the moments of the full average deformation rate tensor, as well as all of the first, second and third fluctuating velocity moments except those involving pressure. The Reynolds number was $Re_\theta = 7634$ or $Re_\tau = 2598$. The present paper gives the measured average dissipation, $\epsilon$ and the derivative moments comprising it. The results are compared with the earlier measurements of Balint, Wallace & Vukolavcevic (J. Fluid Mech. , vol. 228, 1991, pp. 53–86) and Honkan & Andreopoulos (J. Fluid Mech. , vol. 350, 1997, pp. 29–96) at lower Reynolds numbers and to new results from a plane channel flow DNS at comparable Reynolds number. Of special interest is the prediction by George & Castillo (Appl. Mech. Rev. , vol. 50, 1997, pp. 689–729) and Wosnik, Castillo & George (J. Fluid Mech. , vol. 421, 2000, pp. 115–145) that $\epsilon ^+ \propto {x_2^+}^{-1}$ for streamwise homogeneous flows and a nearly indistinguishable power law, $\epsilon \propto {x_2^+}^{\gamma -1}$ , for boundary layers. In spite of the modest Reynolds number, the predictions seem to be correct. Then the statistical character of the velocity derivatives is examined in detail, and a particular problem is identified with the breakdown of local homogeneity inside $x_2^+ = 100$. A more general alternative for partially homogeneous turbulence flows is offered which is consistent with the observations. With the help of DNS, the spatial characteristics of the dissipation very near the wall are also examined in detail. [ABSTRACT FROM AUTHOR]

In this paper, a concept of a floating elastic wave energy converter consisting of a disk-shaped elastic plate is proposed. The floating plate is moored to the seabed through a series of power take-off (PTO) units. A theoretical model based on the linear potential flow theory and eigenfunction matching method is developed to study the hydroelastic characteristics and evaluate wave power absorption of the device. The PTO system is simulated as a discrete PTO, and moreover, it is also modelled as a continuum PTO to represent the case when the PTO system is composed of a large number of PTO units. The continuum PTO approximation is tested against the discrete PTO simulation for accuracy. Two methods are proposed to predict the wave power absorption of the device. After running convergence analysis and model validation, the present model is employed to do a multiparameter impact analysis. The device adopting a continuum PTO system is found to capture wave power efficiently in an extensive range of wave frequencies. For the continuum PTO system, it is theoretically possible to adopt optimised PTO damper and stiffness/mass to guarantee the absorption of 100% of the energy flux available in one circular component of the plane incident wave. [ABSTRACT FROM AUTHOR]

We discuss (i) the measurement, (ii) interpretation and (iii) technical impact of temperature-dependent wall slip and its activation energy for polar and non-polar hydrocarbon Newtonian fluids moving relative to machined metal surfaces. A newly developed apparatus, the slip length tribometer (SLT), overcomes the drawbacks of existing measurement devices in terms of characterising relevant rough surfaces by measuring the slip length at different temperatures over a sufficiently large wetted area. The experimental data show that the bulk viscosity and slip length at the fluid-metal interface is independent of the shear rate up to 105 s-1, being consistent with recent results from molecular dynamics simulations by Mehrnia & Pelz (J. Mol. Liq., vol. 336, 2021, 116589). Furthermore, the activation energies for wall slip and bulk shear determined by means of the SLT differ by a factor of two, i.e. E = 0.5Eµ for non-polar hydrocarbon molecules sliding relative to metal walls. This difference is explained by a generalised Eyring model applied to wall slip. The paper closes with the impact of wall slip on Sommerfeld's similarity theory of tribology and the resulting Stribeck curve (Sommerfeld, Z. Math. Phys., vol. 50, 1904, pp. 97-155; Z. Tech. Phys., vol. 2. Jahrg., 1921; Mechanik der deformierbaren Medien, 1944, Akademische Verlagsgesellschaft Becker & Erler). For this purpose, Reynolds' equation generalised for wall slip is solved in combination with the experimentally determined constitutive relations for bulk shear and wall slip to predict typical characteristics of journal bearings. The results show that, for a typical journal bearing, where the ratio of slip length to average bearing clearance is of the order of 10-2, the influence of wall slip on both load-carrying capacity and dissipation is not negligible. This work combines nanofluidics and tribology in order to provide methods and knowledge for e.g. tailor-made fluids and interfaces. [ABSTRACT FROM AUTHOR]

Previous work suggests that the arrangement of elements in an obstruction may influence the bulk flow velocity through the obstruction, but the physical mechanisms for this influence are not yet clear. This is the motivation for this study, where direct numerical simulation is used to investigate flow through an array of cylinders at a resolution sufficient to observe interactions between wakes of individual elements. The arrangement is altered by varying the gap ratio $G/d$ (1.2 – 18, G is the distance between two adjacent cylinders, d is the cylinder diameter), array-to-element diameter ratio $D/d$ (3.6 – 200, D is the array diameter), and incident flow angle ($0^{\circ} - 30^{\circ}$). Depending on the element arrangement, it is found that the average root-mean-square lift and drag coefficients can vary by an order of magnitude, whilst the average time-mean drag coefficient of individual cylinders ($\overline{C_{d}}$), and the bulk velocity are found to vary by up to $50\,\%$ and a factor of 2, respectively. These arrangement effects are a consequence of the variation in flow and drag characteristics of individual cylinders within the array. The arrangement effects become most critical in the intermediate range of flow blockage parameter $\mathit{\Gamma_{D}^{\prime}} = 0.5-1.5$ ($\mathit{\Gamma_{D}^{\prime}}=\overline{C_{d}}aD/(1-\phi)$ , where a is frontal element area per unit volume, and $\phi$ is solid volume fraction), due to the high variability in element-scale flow characteristics. Across the full range of arrangements modelled, it is confirmed that the bulk velocity is governed by flow blockage parameter but only if the drag coefficient incorporates arrangement effects. Using these results, this paper proposes a framework for describing and predicting flow through an array across a variety of arrangements. [ABSTRACT FROM AUTHOR]

Thin-film equations are utilised in many different areas of fluid dynamics when there exists a direction in which the aspect ratio can be considered small. We consider thin free films with Marangoni effects in the extensional flow regime, where velocity gradients occur predominantly along the film. In practice, because of the local deposition of surfactants or input of energy, asymmetric distributions of surfactants or surface tension more generally, are possible. Such examples include the surface of bubbles and the rupture of thin films. In this study, we consider the asymmetric thin-film equations for extensional flow with Marangoni effects. Concentrating on the case of small Reynolds number $ Re $ , we study the deposition of insoluble surfactants on one side of a liquid sheet otherwise at rest and the resulting thinning and rupture of the sheet. The analogous problem with a uniformly thinning liquid sheet is also considered. In addition, the centreline deformation is discussed. In particular, we show analytically that if the surface tension isotherm $\sigma = \sigma (\varGamma)$ is nonlinear (surface tension $\sigma$ varies with surfactant concentration $\varGamma$), then accounting for top–bottom asymmetry leads to slower (faster) thinning and pinching if $\sigma = \sigma (\varGamma)$ is convex (concave). The analytical progress reported in this paper allows us to discuss the production of satellite drops from rupture via Marangoni effects, which, if relevant to surface bubbles, would be an aerosol production mechanism that is distinct from jet drops and film drops. [ABSTRACT FROM AUTHOR]

Direct numerical simulations (DNS) were carried out to investigate flow control for transition delay using steady blowing/suction strips at the wall of a flared cone at Mach 6 and zero angle of attack. For the numerical investigations of the transition control strategy, the flared cone geometry and the flow conditions of the experiments in the Boeing/Air Force Office of Scientific Research (AFOSR) Mach 6 Quiet Tunnel (BAM6QT) at Purdue University were chosen. For the DNS, transition was initiated by introducing random disturbances at the inflow of the computational domain, emulating 'natural' transition in wind-tunnel experiments caused by free-stream noise. In both wind-tunnel experiments and numerical simulations, streamwise 'hot' streaks were found on the surface of the flared cone, which are caused by a nonlinear interaction of an axisymmetric second-mode wave and a pair of oblique waves of the same frequency ('fundamental resonance'). The objective of the flow control strategy proposed here is to delay the transition onset, and thus mitigate the negative consequences associated with the nonlinear transition stages, i.e. the development of hot streaks and large wall-pressure amplitudes that were observed in experiments and DNS. Our previous so-called 'controlled' transition simulations have shown that flow control using steady blowing and suction strips can lead to a significant delay of the hot streak development on the surface of the flared cone. The simulation results presented in this paper show that this flow control strategy remains effective, even in a natural transition scenario characterized by broadband disturbances. [ABSTRACT FROM AUTHOR]

Wall temperature has a significant effect on shock wave/turbulent boundary layer interactions (STBLIs) and has become a non-negligible factor in the design process of hypersonic vehicles. In this paper, direct numerical simulations are conducted to investigate the wall temperature effects on STBLIs over a 34° compression ramp at Mach number 6. Three values of the wall-to-recovery-temperature ratio (0.50, 0.75 and 1.0) are considered in the simulations. The results show that the size of the separation bubble declines significantly as the wall temperature decreases. This is because the momentum profile of the boundary layer becomes fuller with wall cooling, which means the near-wall fluid has a greater momentum to suppress flow separation. An equation based on the free-interaction theory is proposed to predict the distributions of the wall pressure upstream of the corner at different wall temperatures. The prediction results are generally consistent with the simulation results (Reynolds number Reτ ranges from 160 to 675). In addition, the low-frequency unsteadiness is studied through the weighted power spectral density of the wall pressure and the correlation between the upstream and downstream. The results indicate that the low-frequency motion of the separation shock is mainly driven by the downstream mechanism and that wall cooling can significantly suppress the low-frequency unsteadiness, including the strength and streamwise range of the low-frequency motions. [ABSTRACT FROM AUTHOR]

We consider the long-time propagation of a Boussinesq inertia–buoyancy (large-Reynolds- number) gravity current released from a lock over a downslope of angle $\gamma$ , affected by entrainment and drag. We show that the shallow-water (depth-averaged) equations with a Benjamin-type front-jump condition admit a similarity solution $x_N(t) = K t^{2/3}$ while $h, \phi, u$ change like $t$ to the power of $2/3, -4/3, -1/3$ , respectively; here $x_N, h, \phi, u$ and $t$ are the position of the nose (distance from backwall), thickness, concentration of dense fluid, velocity and time, respectively, and K is a constant. Assuming that $\gamma$ and the coefficients of entrainment and drag are constant, we derive an analytical exact solution for the similarity profiles and show that $K \propto (\tan \gamma)^{1/3}$ ; the driving of the slope is balanced by entrainment and/or drag. The predicted $t^{2/3}$ propagation is in agreement with previously published experimental data but a conclusive quantitative assessment of the present theory cannot be performed due to various uncertainties (discussed in the paper) that must be resolved by future work. [ABSTRACT FROM AUTHOR]

The prototypical diffuse-interface model for incompressible fluid mixtures is the Navier–Stokes Cahn–Hilliard (Allen–Cahn) model. Despite its foundation in continuum mixture theory, it is not fully compatible with this theory due to the diffusive flux approximation. This paper introduces a class of thermodynamically consistent diffuse-interface incompressible fluid mixture models that is fully compatible with the continuum theory of mixtures. The proposed models can be formulated in either constituent or mixture quantities, enabling a direct comparison with the Navier–Stokes Cahn–Hilliard (Allen–Cahn) model with non-matching densities. This comparison reveals the key modelling simplifications employed in the latter. [ABSTRACT FROM AUTHOR]

Serrations are commonly employed to mitigate the turbulent boundary layer trailing-edge noise. However, significant discrepancies persist between model predictions and experimental observations. In this paper, we show that this results from the frozen turbulence assumption. A fully developed turbulent boundary layer over a flat plate is first simulated using the large-eddy simulation method, with the turbulence at the inlet generated using the digital filter method. The space–time correlations and spectral characteristics of wall pressure fluctuations are examined. The simulation results demonstrate that the coherence function decays in the streamwise direction, deviating from the constant value of unity assumed in the frozen turbulence assumption. By considering an exponential decay function, we relax the frozen turbulence assumption and develop a prediction model that accounts for the intrinsic non-frozen nature of turbulent boundary layers. To facilitate a direct comparison with frozen models, a correction coefficient is introduced to account for the influence of non-frozen turbulence. The comparison between the new and original models demonstrates that the new model predicts lower noise reductions, aligning more closely with the experimental observations. The physical mechanism underlying the overprediction of the noise model assuming frozen turbulence is discussed. The overprediction is due to the decoherence of the phase variation along the serrated trailing edge. Consequently, the ratio of the serration amplitude to the streamwise frequency-dependent correlation length is identified as a crucial parameter in determining the correct prediction of far-field noise. [ABSTRACT FROM AUTHOR]

The clustering of debris floating on liquid interfaces such as water surfaces is a complex phenomenon that finds its applications in numerous examples from industrial processing and environmental systems. The recent paper by Shin & Coletti (J. Fluid Mech. , vol. 984, 2024, R7) presents an experimental campaign investigating the three effects of turbulence, particle interactions and interfacial effects, to elucidate how the three force scales drag, capillary forces and lubrication give rise to three distinct regimes of clustering in dense suspensions. The study, hence, provides a useful systematic to categorize the clustering mechanisms. As an important finding, it is shown that, depending on volume fraction and non-dimensional turbulent shear, particles either tend to cluster into aggregate sizes larger than the Kolmogorov scale or can break into pieces that are as small as the primary particle size. [ABSTRACT FROM AUTHOR]

Understanding settling motion of coral grains is important in terms of protection of coral reef systems and resotoration of the associated ecosystems. In this paper, a series of laboratory experiments was conducted to investigate the settling motion, using optical microscopy to measure shape parameters of coral grains and the particle-filtering-based object tracking to reconstruct the three-dimensional trajectory. Three characteristic descent regimes, namely, tumbling, chaotic and fluttering, are classified based on the three-dimensional trajectory, the spiral radius variation and the velocity spectrum. It is demonstrated that if one randomly picks up one coral grain, then the probabilities of occurrence of the three regimes are approximately $26\,\%$ , $42\,\%$ and $32\,\%$ , respectively. We have shown that first, the dimensionless settling velocity generally increases with the non-dimensional diameter and Corey shape factor and second, the drag coefficient generally decreases with the Reynolds number and Corey shape factor. Based on this, the applicability of existing models on predicting settling velocity and drag coefficient for coral grains is demonstrated further. Finally, we have proposed extended models for predicting the settling velocity. This study contributes to better understanding of settling motion and improves our predictive capacity of settling velocity for coral grains with complex geometry. [ABSTRACT FROM AUTHOR]

This paper deals with the construction of the tip asymptotes for a hydraulic fracture deflating in a permeable elastic medium. Specifically, the paper describes the changing nature of the asymptotic fields during the arrest and recession phases following propagation of the fracture after fluid injection has ended. It shows that as the fracture deflates in the arrest phase, the region of dominance of the linear elastic fracture mechanics tip asymptote $w\sim x^{1/2}$ of the fracture aperture $w$ with distance $x$ from the front shrinks to the benefit of an intermediate asymptote $w\sim x^{3/4}$. Hence only the velocity-independent $3/4$ asymptote is left at the arrest–recession transition. Furthermore, with increasing receding velocity of the front, a linear asymptote $w\sim x$ develops progressively at the fracture tip, with $w\sim x^{3/4}$ again becoming an intermediate asymptote. These universal multiscale asymptotes for the arrest and recession phases are key to determining, in combination with a computational algorithm that can simulate the evolution of a finite fracture, the decaying stress intensity factor during arrest, the time at which the fracture transitions from arrest to recession, and the negative front velocity during recession. [ABSTRACT FROM AUTHOR]

This paper describes a numerical investigation on the effects of small to large bluntness as well as the angle of incidence on the leading-edge separation in a laminar hypersonic flow. The results show that both bluntness and incidence strongly influence separation characteristics. A combined bluntness and incidence parameter is proposed and applied to plateau pressures in the separated region and is shown to demarcate effects of small and large bluntness at different angles of incidence. The investigation also showed profound changes in the internal structure of the separation bubble with changes in incidence and bluntness. The significance of the relationship between the two shear stress minima and the separation length is highlighted. [ABSTRACT FROM AUTHOR]

This paper theoretically studies the effect of eccentricity on the conditions of capillary emptying (determined by critical Bond number) in a horizontal annular tube in a downward gravity field. Experiments are conducted to compare with theoretical results. We find that non-horizontal eccentricity can lead to the occurrence of a re-entrant liquid-state transition (from liquid non-occlusion to liquid plug to liquid non-occlusion) with increasing Bond number, when the eccentricity (e) or inner-to-outer radius ratio (χ) is large enough, and the two liquid non-occlusion states correspond to different emptying mechanisms dominated by the gravity effect and the 'wedge' effect, respectively. Existence of the re-entrant transition is accompanied by occurrence of unconditional liquid non-occlusion at large enough or small enough contact angles regardless of Bond numbers. The critical Bond numbers at a contact angle γ for vertical upward eccentricity are equal to those at a contact angle 180° − γ for vertical downward eccentricity. In a parameter space (γ, e/(1 − χ)), the region with the re-entrant transition becomes larger with the eccentric angle varying from 0° (horizontal) to 90° (vertical). Optimization of geometrical parameters and inner and outer contact angles can lead to better effect of capillary emptying. This paper provides a very effective scheme for removing a liquid blockage from a capillary in optofluidics/microfluidics. [ABSTRACT FROM AUTHOR]

In this paper, the instability of shallow-water shear flow with a sheared parallel magnetic field is studied. Waves propagating in such magnetic shear flows encounter critical levels where the phase velocity relative to the basic flow, c − U( y), matches the Alfvén wave velocities ±B( y)/√μρ, based on the local magnetic field B( y), the magnetic permeability μ, and the mass density of the fluid ρ. It is shown that when the two critical levels are close to each other, the critical layer can generate an instability. The instability problem is solved, combining asymptotic solutions at large wavenumbers and numerical solutions, and the mechanism of instability explained using the conservation of momentum. For the shallow-water magnetohydrodynamic system, the paper gives the general form of the local differential equation governing such coalescing critical layers for any generic field and flow profiles, and determines precisely how the magnetic field modifies the purely hydrodynamic stability criterion based on the potential vorticity gradient in the critical layer. The curvature of the magnetic field profile, or equivalently the electric current gradient J′ = −B″/μ in the critical layer, is found to play a complementary role in the instability [ABSTRACT FROM AUTHOR]

We rework some of the die-swell singularity analysis for Stokes flow, originally by Ramalingam (Ramalingam, 1994 Fiber spinning and rheology of liquid-crystalline polymers, PhD thesis, Massachusetts Institute of Technology) in appendix A of his PhD thesis, in an attempt to demonstrate that for capillary numbers in the range (0,∞) the curvature may enter into the normal stress balance on the free surface and lead to separation angles exceeding 180◦ and infinite curvature at the separation point. The singular coefficients in the asymptotic solution and the free surface shape in a neighbourhood of the separation point cannot be determined by a local analysis of the Michael type (Michael, Mathematika, vol. 5, 1958, pp. 82-84) but must be found from matching with the solution valid away from the die edge. The numerical method that we use in the truncated die-swell domain is a boundary element method incorporating the singular solution near the separation point. Although there is some variation in the extrudate swell ratios at different capillary numbers reported in the numerical literature, our results for capillary numbers Ca from 1 to 1000 are within the range of values published in earlier papers. The computed separation angles at different values of Ca agree well with the range of separation angles to be found in experimental and numerical papers. The separation angle appears to converge to a value different from 180◦ as Ca increases, leading us to conclude that the case of zero surface tension (Ca=∞, with corresponding separation angle of 180◦), is a singular limit. [ABSTRACT FROM AUTHOR]

In the asymptotic theory of interaction noise from contra-rotating propellers with many blades, previous work in the frequency domain has shown that, for each combination mode/tone, the critical points that dominate the acoustic radiation can be linked to two criteria (sonic and normal-edge) and to a radial event line that spins around the annulus at the same speed as the mode. Thus the speed is different for each combination tone. In real time, however, the interactions precess around the annulus at a single speed, governed by the 'firing order' of the interactions, with that speed being (in general) considerably different from that of either the front or rear blade rows. The precession of the interaction is described here in detail and then demonstrated by application to three relevant architectures, including a rotor–stator configuration. The paper then considers how the blade leading-edge design affects the radial variation in the interaction location and analyses the interactions from the viewpoint of a far-field observer. The paper also connects previous time- and frequency-domain results by showing that the sonic and normal-edge criteria can be derived in the time domain using the precession speed. The case of equal blade numbers is also included, for which the precession speed becomes infinite but for which, nonetheless, the sonic and normal-edge criteria still apply. [ABSTRACT FROM AUTHOR]

With the growing interest in scale-resolving simulations of spatially evolving boundary layers, synthetic turbulence generation (STG) has become a valuable tool for providing unsteady turbulent boundary conditions through a sum over a finite number of spatio-temporal Fourier modes with amplitude, direction and phase determined by a random number set. Recent developments of STG methods are designed to match target profiles for anisotropic and inhomogeneous Reynolds stresses. In this paper, it is shown that, for practical values of the number of modes, a given set of random numbers may produce Reynolds stress profiles that are 30 % off their target. To remedy this situation, the error in the STG stress prediction is decomposed into a steady-state bias and a purely unsteady part affecting the time convergence. Direct relationships between the random number vectors and both types of error are developed, allowing large collections of random number sets to be rapidly scanned and the best performers selected for a much improved agreement with the target. The process is verified for the inflow to a direct numerical simulation of a flat plate at $Re_\theta = 1000$. This paper demonstrates sufficient time convergence over a few flow-through times as well as a correction of the method's biases. [ABSTRACT FROM AUTHOR]

This paper proposes a low-divergence method to generate inhomogeneous and anisotropic turbulence. Based on the idea of correlation reconstruction, the proposed method uses the Cholesky decomposition matrix to re-establish turbulence correlation functions. This is in contrast with the time-consuming procedure used in conventional methods to solve eigenvalues and eigenvectors in each location required by coordinate transformation, thereby reducing the computational complexity and improving the efficiency of synthetic turbulence generation. The proposed method is based on the classical spectrum-based method that is widely used to generate homogeneous and isotropic turbulence. By adjusting the generation strategy of specific random vectors, inhomogeneous and anisotropic turbulence with a relatively low divergence level can be obtained in practice, with almost no additional computational burden. Two versions of the proposed method are presented: the inverter and shifter versions. Both the versions are highly efficient, easy to implement, and compatible with high-performance computing. This method is also suitable for providing high-quality initial or boundary conditions for scale-resolving turbulence simulations with large grid numbers (such as direct numerical simulations or large eddy simulations); it can be rapidly implemented using various open-source computational fluid dynamics codes or common commercial software. [ABSTRACT FROM AUTHOR]

This paper reports several new classes of unstable recurrent solutions of the two-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions are in many ways analogous to recurrent solutions of the Navier–Stokes equation which are often referred to as exact coherent structures. In particular, we find that recurrent solutions of the Euler equation are dynamically relevant: they faithfully reproduce large-scale flows in simulations of turbulence at very high Reynolds numbers. On the other hand, these solutions have a number of properties which distinguish them from their Navier–Stokes counterparts. First of all, recurrent solutions of the Euler equation come in infinite-dimensional continuous families. Second, solutions of different types are connected, e.g. an equilibrium can be smoothly continued to a travelling wave or a time-periodic state. Third, and most important, they are only weakly unstable and, as a result, fully developed turbulence mimics some of these solutions remarkably frequently and over unexpectedly long temporal intervals. [ABSTRACT FROM AUTHOR]

A present paper generalizes the work of Tyvand & Miloh (J. Fluid Mech. , vol. 286, 1995, pp. 67–101) on the problem of the free surface flow generated by a submerged circular cylinder moving impulsively with constant velocity to the case of a cylinder moving with both initial velocity and acceleration. The nonlinear small-time asymptotic solution for the velocity potential, free surface elevation and hydrodynamic pressure force is calculated analytically in bipolar coordinates for a cylinder of arbitrary radius. The analytical solution is obtained to the leading order of nonlinear interaction between initial impulsive velocity and initial impulsive acceleration directed at arbitrary angles. In the special case of the motion with constant acceleration, the complete fourth-order free-surface flow problem is solved and the associated second-order hydrodynamic force is computed. The leading-order contributions to the free surface elevation due to the constant velocity and constant acceleration are compared for finite rectilinear cylinder displacements. The role of constant acceleration consists of two contributions to the leading nonlinear terms, where the amplitude of the first one is 25 % below the case of constant velocity while the amplitude of the other exceeds it by 50 %. [ABSTRACT FROM AUTHOR]

It is known that the disintegration of vertical liquid curtains (sheets) is affected crucially by the amplification of free edge holes forming inside the curtain. This paper aims to investigate the influence of the hole expansion dynamics, driven by the so-called rim retraction, on the breakup of a liquid curtain, in both supercritical (Weber number $We > 1$) and subcritical ($We) conditions. The analysis is based on three-dimensional direct numerical simulations. For a selected supercritical configuration, the steady flow topology is first analysed. The investigation reveals the classic triangular shape regime of the steady curtain, due to the surface-tension-induced borders retraction towards its centre plane. The unsteady dynamics is then investigated as the curtain response to a hole perturbation introduced artificially in the steady flow configuration. The hole evolution determines a rim retraction phenomenon inside the curtain, which is influenced by both capillary and gravity forces. In supercritical conditions, the hole does not influence the curtain flow dynamics in the long-time limit. By reducing the Weber number slightly under the critical threshold ($We=1$), the initial amplification rate of the hole area increases, due to the stronger retraction effect of surface tension acting on the hole rims. The free hole expansion in fully subcritical conditions ($We) is investigated finally by simulating an edge-free curtain flow. As $We$ decreases progressively, the hole expands while it is convected downstream by gravity acceleration. In the range $0.4 , the subcritical curtain returns to the intact unperturbed configuration after the hole expulsion at the downstream outflow. For $We , the surface tension force becomes strong enough to reverse the gravitational motion of the hole top point, which retracts upstream towards the sheet inlet section while expanding along the lateral directions. This last phenomenon causes finally the breakup of the curtain, which results in a columnar regime strictly resembling similar experimental findings of the literature. [ABSTRACT FROM AUTHOR]

Electrophoresis is the motion of a charged colloidal particle in an electrolyte under an applied electric field. The electrophoretic velocity of a spherical particle depends on the dimensionless electric field strength $\beta =a^*e^*E_\infty ^*/k_B^*T^*$ , defined as the ratio of the product of the applied electric field magnitude $E_\infty ^*$ and particle radius $a^*$ , to the thermal voltage $k_B^*T^*/e^*$ , where $k_B^*$ is Boltzmann's constant, $T^*$ is the absolute temperature, and $e^*$ is the charge on a proton. In this paper, we develop a spectral element algorithm to compute the electrophoretic velocity of a spherical, rigid, dielectric particle, of fixed dimensionless surface charge density $\sigma$ over a wide range of $\beta$. Here, $\sigma =(e^*a^*/\epsilon ^*k_B^*T^*)\sigma ^*$ , where $\sigma ^*$ is the dimensional surface charge density, and $\epsilon ^*$ is the permittivity of the electrolyte. For moderately charged particles ($\sigma ={O}(1)$), the electrophoretic velocity is linear in $\beta$ when $\beta \ll 1$ , and its dependence on the ratio of the Debye length ($1/\kappa ^*$) to particle radius (denoted by $\delta =1/(\kappa ^*a^*)$) agrees with Henry's formula. As $\beta$ increases, the nonlinear contribution to the electrophoretic velocity becomes prominent, and the onset of this behaviour is $\delta$ -dependent. For $\beta \gg 1$ , the electrophoretic velocity again becomes linear in field strength, approaching the Hückel limit of electrophoresis in a dielectric medium, for all $\delta$. For highly charged particles ($\sigma \gg 1$) in the thin-Debye-layer limit ($\delta \ll 1$), our computations are in good agreement with recent experimental and asymptotic results. [ABSTRACT FROM AUTHOR]

Engineering flow systems operating under low pressures and/or at the micro/nano scale generally include a physically adsorbed gas layer next to the surface. In this paper, we develop a scattering kernel that accounts for the effect of adsorption, arising from van der Waals interactions, on the dynamics of molecules impinging on solid smooth surfaces. In the limit of low bulk density, surface adsorption becomes negligible and the scattering kernel recovers consistently the Cercignani–Lampis model, which best describes molecular collisions with a clean, smooth surface. In the limit of high bulk density, a dense adsorbed molecular layer forms next to the surface and its presence is picked up by the Maxwell model with complete diffuse reflection, which better captures the multiple collisions suffered by molecules. A weight coefficient based on the Langmuir adsorption isotherm is incorporated into the modelling to handle the transition between these two limiting conditions of low and high densities. The proposed model is validated against high-fidelity molecular dynamics simulations that are performed for a variety of gas–surface combinations and adsorbed molecular layers with different densities. It is shown that the proposed model very well captures the scattering patterns of beams of gas molecules at different velocities impinging on surfaces, as well as momentum and energy accommodation coefficients in the entire range of explored conditions. [ABSTRACT FROM AUTHOR]