In this paper, we construct an accurate linear model describing the propagation of both acoustic and gravity waves in water. This original model is obtained by the linearization of the compressible Euler equations, written in Lagrangian coordinates. The system is studied in the isentropic case, with a free surface, an arbitrary bathymetry, and vertical variations of the background temperature and density. We show that our model is an extension of some models from the literature to the case of a non-barotropic fluid with a variable sound speed. Other models from the literature are recovered from our model through two asymptotic analyses, one for the incompressible regime and one for the acoustic regime. We also propose a method to write the model in Eulerian coordinates. Our model includes many physical properties, such as the existence of internal gravity waves or the variation of the sound speed with depth.

Owing to the Taylor–Proudman theorem, it is generally believed that rotating flows should have two-dimensional dynamics for rapid background rotation. Yet, we show that two infinitely long counter-rotating vertical vortices always remain unstable to three-dimensional perturbations even for large rotation rate about the vertical axis. The dominant instability consists of quasi-antisymmetric displacements of the two vortices. Its growth rate is independent of the rotation rate when it is sufficiently large, while the most amplified vertical wavelength scales like the rotation rate. Direct numerical simulations show that the instability leads ultimately to a full three-dimensional breakdown of the vortex pair. In other words, a two-dimensional vortex pair will spontaneously develop three-dimensional variations even in the limit of infinite rotation rate but the wavelength will tend to infinity. This implies that the Taylor–Proudman theorem can be strictly valid only in vertically bounded flows. The scaling for the wavelength is next generalized by showing that the typical vertical scale in rapidly rotating unbounded flows is $L_v \sim L_h/Ro$, where $L_h$ is the horizontal scale and $Ro$ the Rossby number. This scaling law is shown to derive from a self-similarity of the Navier–Stokes equations for $Ro \ll 1$. The resulting reduced equations are identical to those obtained first by Julien et al. (Theor. Comput. Fluid Dyn., vol. 11, issue 3–4, 1998, pp. 251–261) and Nazarenko & Schekochihin (J. Fluid Mech., vol. 677, 2011, pp. 134–153) by means of multiscale analyses in the cases of rotating convection or turbulence. The self-similarity demonstrated herein suggests that these reduced equations are valid for any rapidly rotating unbounded flow.

We report numerical simulations confirming the predictions in Gordillo & Riboux (J. Fluid Mech., vol. 941, 2022, A10), where we elucidated the lubrication mechanism by which a drop of a low-viscosity liquid impacting over a smooth solid substrate skates over a thin gas film that prevents contact with the wall. Moreover, with the purpose of explaining the so-called lift-off mechanism reported in Kolinski et al. (Phys. Rev. Lett., vol. 112, issue 13, 2014, 134501), we extend our previous findings and derive expressions for the time-varying thickness of the gas layer at the region where the distance to the wall is minimum, finding good agreement with the numerical results. In addition, we report that our predictions for the minimum thickness of the gas film separating a falling drop from a wall at room temperature follow closely the experimental values when gas kinetic effects are retained in the analysis, and also report that the analogous equation for the minimum thickness of the vapour layer formed after a drop impacts a superheated wall predicts well the experimental measurements.

We calculate the net energy per unit time exchanged between two sets of modes in a generic system governed by a three-wave kinetic equation. Our calculation is based on the property of detailed energy conservation of the triadic resonant interactions. In a first application to isotropic systems, we re-derive the previously used formula for the energy flux as a particular case for adjacent sets. We then exploit the new formalism to quantify the level of locality of the energy transfers in the example of surface capillary waves. A second application to anisotropic wave systems expands the currently available set of tools to investigate magnitude and direction of the energy fluxes in these systems. We illustrate the use of the formalism by characterizing the energy pathways in the oceanic internal wavefield. Our proposed approach, unlike traditional approaches, is not limited to stationarity, scale invariance and strict locality. In addition, we define a number $w$ that quantifies the scale separation necessary for two sets of modes to having negligible mutual energy exchange, with potential consequences in the interpretation of wave turbulence experiments. The methodology presented here provides a general, simple and systematic approach to energy fluxes in wave turbulence.

Data from an energetic tidal flow are used to investigate the appropriateness of the classical scaling of wall turbulence for very high Reynolds numbers and fully rough conditions. The boundary layer occupied the entire channel depth and the Reynolds numbers were several orders of magnitude larger than typically attained in the laboratory. Profiles of the mean velocity, turbulence quantities and spectra exhibit consistencies with the wall-similarity hypothesis and the attached-eddy model, as well as the universality of the near-wall turbulence structure for geophysical flows. The wall-normal velocity spectra and intensities near the free surface are also strongly attenuated at low wavenumbers, consistent with the constraints imposed by any boundary which may be approximated as a plane slip surface. The results can be used to inform the development of turbulence inflow models for assessing the dynamic loading on tidal turbines and the layout of tidal energy farms.

We investigate the stability of katabatic slope flows over an infinitely wide and uniformly cooled planar surface subject to a downslope uniform ambient wind aloft. We adopt an extension of Prandtl’s original model for slope flows (Lykosov & Gutman, Izv. Acad. Sci. USSR Atmos. Ocean. Phys., vol. 8 (8), 1972, pp. 799–809) to derive the base flow, which constitutes an interesting basic state in stability analysis because it cannot be reduced to a single universal form independent of external parameters. We apply a linear modal analysis to this basic state to demonstrate that for a fixed Prandtl number and slope angle, two independent dimensionless parameters are sufficient to describe the flow stability. One of these parameters is the stratification perturbation number that we have introduced in Xiao & Senocak (J. Fluid Mech., vol. 865, 2019, R2). The second parameter, which we will henceforth designate the wind forcing number, is hitherto uncharted and can be interpreted as the ratio of the kinetic energy of the ambient wind aloft to the damping due to viscosity and the stabilising effect of the background stratification. For a fixed Prandtl number, stationary transverse and travelling longitudinal modes of instabilities can emerge, depending on the value of the slope angle and the aforementioned dimensionless numbers. The influence of ambient wind forcing on the base flow’s stability is complicated, as the ambient wind can be both stabilising as well as destabilising for a certain range of the parameters. Our results constitute a strong counterevidence against the current practice of relying solely on the gradient Richardson number to describe the dynamic stability of stratified atmospheric slope flows.

The dynamics and nonlinear wave forcing of a flexible floating structure are investigated experimentally and numerically. The floater was designed to match sub-harmonic rigid-body natural frequencies of typical floating wind turbine substructures, with the addition of a flexible bending mode. Experiments were carried out for three sea states with phase-shifted input signals to allow harmonic separation of the measured response. We find for the weakest sea states that sub-harmonic rigid-body motion is driven by even-harmonic difference frequency forcing, and by linear forcing for the strongest sea state. The flexible mode was tested in a soft, linearly forced layout, and a stiff layout, forced by second-, third- and fourth-harmonic frequency content, for increasing severity of the sea state. Further insight is gained by analysis of the amplitude scaling of the resonant response. A new simplified approach is proposed and compared with the recent method of Orszaghova et al. (J. Fluid Mech., vol. 929, 2021, A32). We find that resonant surge and pitch motions are dominated by even-harmonic potential-flow forcing and that odd-harmonic response is mainly potential-flow driven in surge and mainly drag driven in pitch. The measured responses are reproduced numerically with second-order forcing and quadratic drag loads, using a recent and computationally efficient calculation method, extended here for the heave, pitch and flexible motions. We are able to reproduce the response statistics and power spectra for the measurements, including the subharmonic pitch and heave modes and the flexible mode. Deeper analysis reveals that inaccuracies in the even-harmonic forcing content can be compensated by the odd-harmonic loads.

Phase-averaged and cycle-to-cycle analysis of key contributors to sound production in phonation is examined in a scaled-up vocal-fold model. Simultaneous temporally and spatially resolved pressure and velocity measurements permitted examination of each term in the streamwise integral momentum equation. The relative sizes of these terms were used to address the issue of whether transglottal pressure is a surrogate for vocal-fold drag, a quantity directly related to sound production. Further, time traces of transglottal pressure and volume flow rate provided insight into the role of cycle-to-cycle variations in voiced sound production which affect voice quality. Experiments were conducted using a 10× scaled-up model in a free-surface water tunnel. Two-dimensional vocal-fold models with semi-circular ends inside a square duct were driven with constant opening and closing speeds. The time from opening to closed, To, was half the oscillation period. Time-resolved digital particle image velocimetry (DPIV) and pressure measurements along the duct centreline were made for 3650 ≤ Re ≤ 8100 and equivalent life frequencies from 52.5 to 97.5 Hz. Results showed that transglottal pressure does serve as a surrogate for the vocal-fold drag. However, smaller but non-negligible momentum flux and inertia terms, caused by the jet and vocal-fold motions, may also contribute to vocal-fold drag. Further, cycle-to-cycle variations including jet switching and modulation are inherent in flows of this type despite their high degrees of symmetry and repeatability. The origins of these variations and their potential role in sound production and voice quality are discussed.

Transient behaviours during spin-up in rotating Rayleigh–Bénard convection (RBC) with imposed rotation were quantitatively investigated in laboratory experiments. Horizontal and vertical velocity fields were measured by particle image velocimetry with water as the test fluid. Varying the aspect ratio, Rayleigh number and Taylor number, a total of twenty parameters were systematically explored. Toroidal and spiral rolls were formed when the flow reached the rigid-body rotation state, and creation of these structures propagated from the rim towards the internal regions together with the development of the spin-up. Alternate alignments of rolls with opposite meridional circulation transported azimuthal momentum in the rigid-body rotation, and a meandering velocity profile in the radial direction, induced Kelvin–Helmholtz (KH) instability generating azimuthally aligned vortices. The vortices progressively decreased in horizontal dimensions with the wall-to-centre propagation of the vortex formation, but the vortical structures remain larger than the columnar vortices formed in the equilibrium state of a rotating RBC. At the intermediate radius of the fluid layer, the wall-to-centre propagation of the roll formation was overtaken by that of the KH vortex formation. Farther into the interior region, thermal plumes forming columnar vortices were generated as separations of the thermal boundary layers, and the system reached an equilibrium state of rotating RBC dominated by columnar vortices. Use of a fluid vessel with a moderate aspect ratio clarified these transitions to occur in a stepwise fashion, and a spin-up time scale unique in the rotating RBC was found to be from a few to 10 times the Ekman time scale.

To assess how the presence of surfactant in lung airways alters the flow of mucus that leads to plug formation and airway closure, we investigate the effect of insoluble surfactant on the instability of a viscoplastic liquid coating the interior of a cylindrical tube. Evolution equations for the layer thickness using thin-film and long-wave approximations are derived that incorporate yield-stress effects and capillary and Marangoni forces. Using numerical simulations and asymptotic analysis of the thin-film system, we quantify how the presence of surfactant slows growth of the Rayleigh–Plateau instability, increases the size of initial perturbation required to trigger instability and decreases the final peak height of the layer. When the surfactant strength is large, the thin-film dynamics coincide with the dynamics of a surfactant-free layer but with time slowed by a factor of four and the capillary Bingham number, a parameter proportional to the yield stress, exactly doubled. By solving the long-wave equations numerically, we quantify how increasing surfactant strength can increase the critical layer thickness for plug formation to occur and delay plugging. The previously established effect of the yield stress in suppressing plug formation (Shemilt et al., J. Fluid Mech., vol. 944, 2022, A22) is shown to be amplified by introducing surfactant. We discuss the implications of these results for understanding the impact of surfactant deficiency and increased mucus yield stress in obstructive lung diseases.

A new two-equation model for gravity-driven liquid film flow based on the long-wave expansion has been derived. The novelty of the model consists in using a base velocity profile combining parabolic (Ruyer-Quil & Manneville, Eur. Phys. J. B, vol. 15, issue 2, 2000, pp. 357–369) and ellipse (Usha et al., Phys. Fluids, vol. 32, issue 1, 2020, 013603) profile functions in the wall-normal coordinate. The dependence on a free parameter $A$ related to the eccentricity of an ellipse serves as an adjustable parameter. The resulting models are consistent at $O(\varepsilon )$ for inertia terms and at $O(\varepsilon ^2)$ for viscous diffusion effects, and predict accurately the primary instability. Appropriate tuning of the adjustable parameter helps to recover accurate predictions for the asymptotic wave celerity of nonlinear solitary waves. Further, the model is shown to capture the closed separation vortices that can form underneath the troughs of precursory capillary ripples.

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.

The first long-lived turbulent structures observable in planar shear flows take the form of localized stripes, inclined with respect to the mean flow direction. The dynamics of these stripes is central to transition, and recent studies proposed an analogy to directed percolation where the stripes’ proliferation is ultimately responsible for the turbulence becoming sustained. In the present study we focus on the internal stripe dynamics as well as on the eventual stripe expansion, and we compare the underlying mechanisms in pressure- and shear-driven planar flows, respectively, plane-Poiseuille and plane-Couette flow. Despite the similarities of the overall laminar–turbulence patterns, the stripe proliferation processes in the two cases are fundamentally different. Starting from the growth and sustenance of individual stripes, we find that in plane-Couette flow new streaks are created stochastically throughout the stripe whereas in plane-Poiseuille flow streak creation is deterministic and occurs locally at the downstream tip. Because of the up/downstream symmetry, Couette stripes, in contrast to Poiseuille stripes, have two weak and two strong laminar turbulent interfaces. These differences in symmetry as well as in internal growth give rise to two fundamentally different stripe splitting mechanisms. In plane-Poiseuille flow splitting is connected to the elongational growth of the original stripe, and it results from a break-off/shedding of the stripe's tail. In plane-Couette flow splitting follows from a broadening of the original stripe and a division along the stripe into two slimmer stripes.

We analyse a way to make flight vehicles harvest energy from homogeneous turbulence by fast tracking in the way that falling inertial particles do. Mean air speed increases relative to flight through quiescent fluid when turbulent eddies sweep particles and vehicles along in a productive way. Once swept, inertia tends to carry a vehicle into tailwinds more often than headwinds. We introduce a forcing that rescales the effective inertia of rotorcraft in computer simulations. Given a certain thrust and effective inertia, we find that flight energy consumption can be calculated from measurements of mean particle settling velocities and acceleration variances alone, without the need for other information. In calculations using a turbulence model, we optimize the balance between the work performed to generate the forcing and the advantages induced by fast tracking. The results show net energy reductions of up to approximately 10 % relative to flight through quiescent fluid and mean velocities up to 40 % higher. The forcing expands the range of conditions under which fast tracking operates by a factor of approximately ten. We discuss how the mechanism can operate for any vehicle, how it may be even more effective in real turbulence and for fixed-wing aircraft and how modifications might yield yet greater performance.

Hydrodynamic forces acting on a neutrally buoyant spherical particle immersed in a wall-bounded axisymmetric stagnation-point flow (Hiemenz–Homann flow) are predicted, based on a suitable form of the reciprocal theorem. An approximate algebraic form of the undisturbed velocity field is set up, mimicking the gradual transition of the actual carrying flow throughout the boundary layer, from a pure linear straining flow in the bulk to a parabolic flow at the wall. The particle Reynolds number is assumed to be small and predictions based on the creeping-flow assumption are first derived. Then, inertial corrections are computed, assuming that the particle stands close enough to the wall for the latter to be in the inner region of the disturbance. Predictions for the time-dependent slip velocity between the particle and ambient fluid are obtained in the form of a differential equation, first assuming that the particle moves along the flow symmetry axis, then extending the analysis to particles released at an arbitrary radial position. In the former case, these predictions are compared with results provided by numerical simulations. When the strain-based Reynolds number (built on the particle radius and strain rate in the bulk) exceeds $0.1$, finite-inertia effects due to particle–wall interactions and to the relative acceleration between the particle and fluid are found to substantially modify the way the slip velocity varies with the distance to the wall.

A general mixed kinetic-diffusion boundary condition is formulated to account for the out-of-equilibrium kinetics in the Knudsen layer. The mixed boundary condition is used to investigate the problem of quasi-steady evaporation of a droplet in an infinite domain containing inert gases. The widely adopted local thermodynamic equilibrium assumption is found to be the limiting case of infinitely large kinetic Péclet number ${{Pe}_k}$, and it introduces significant error for ${{Pe}_k} \leqslant O(10)$, which corresponds to a typical droplet radius $a$ of a few micrometres or smaller. When compared with experimental data, solutions based on the mixed boundary condition, which take into account the temperature jump across the Knudsen layer, better predict the time evolution of $a$ than the classical $D^2$-law (i.e. $a^2 \propto t$, where $t$ denotes time). In the slow evaporation limit, an analytical solution is obtained by linearising the full formulation about the equilibrium condition, which shows that the $D^2$-law can be recovered only in the large ${{Pe}_k}$ limit. For small ${{Pe}_k}$, where the process is dominated by kinetics, a linear relation, i.e. $a \propto t$, emerges. When the gas phase density approaches the liquid density (e.g. at high-pressure or low-temperature conditions), the increase in the chemical potential of the liquid phase due to the presence of inert gases needs to be accounted for when formulating the mixed boundary condition, an effect largely ignored in the literature so far.

Comprehensive linear stability study of flow in an annular layer of electrolyte driven by the action of the Lorentz force is conducted following the analysis of steady axisymmetric solutions of Suslov et al. (J. Fluid Mech., vol. 828, 2017, pp. 573–600). It is shown that an experimentally observed instability in the form of anticyclonic moving vortices reported in Pérez-Barrera et al. (Magnetohydrodynamics, vol. 51 (2), 2015, pp. 203–213) develops on a background of the basic flow consisting of two tori with the opposite azimuthal vorticity components. It is found that, while the background flow is driven electromagnetically, the appearance of vortices is purely due to hydrodynamic effects: shear of the flow and centrifugal inertial forcing. The current study has also revealed that the unstable two-torus basic flow has a stable single-torus counterpart, both emanating from a saddle-node bifurcation of steady states when the Lorentz force is sufficiently strong. The transition from a one-torus to two-torus flow at weaker forcing is abrupt and leads to the appearance of vortices as soon as it occurs. The ranges of layer depths and Reynolds numbers for which vortices develop on a steady background are determined. Subsequently, weakly nonlinear amplitude expansion is used to find an approximate unsteady solution beyond the saddle-node bifurcation.