This study explores experimentally the flows driven by precession in an oblate spheroid, in the vicinity of the possible resonance with the tilt-over mode. Two main phenomena are reported, combining observations and velocity measurements. First, a hysteretic cycle is quantitatively described between two uniform vorticity solutions, in good agreement with the historical analytical study of Busse (J. Fluid Mech., vol. 33, 1968, pp. 739–752). We then address the destabilization of each branch at low enough Ekman number. We confirm the possible presence of a so-called conical shear instability, recently depicted in the sphere by Lin et al. (Phys. Fluids, vol. 27, 2015, 046601) and in the spheroid by Horimoto et al. (Phys. Rev. Fluids, vol. 5, 2020, 063901). However, available measurements in the accessible parameter range are not sufficient to definitively discard an elliptical or shear origin of the excited instabilities in the spheroid, as first introduced by Kerswell (Geophys. Astrophys. Fluid Dyn., vol. 72, 1993, pp. 107–144).

The paper deals with the resonance oscillations of a drop (bubble) surrounded by a fluid of different density in a container subjected to small amplitude vibrations in zero gravity conditions. The drop size is considered to be large in comparison with both the vibration amplitude and the thickness of viscous Stokes layers. The calculations for parametrically excited oscillations of the drop are carried out in the linear approximation, for inviscid and low viscous media, neglecting compressibility effects. The resonant oscillation is a doublet of neighbouring modes of eigen-oscillations of the drop, for which the sum of frequencies coincides with the frequency of the forced vibrations. This means that the basic state becomes unstable against quasi-periodic oscillations. The finite viscosity implies a finite threshold for the excitation of resonance. On the other hand, the viscosity plays a destabilizing role; at non-zero (even infinitesimal) viscosity the width of the instability frequency range turns out to be greater than in the case of inviscid fluids.

In this work, the classic problem of the aeroacoustic instability occurring in deep cavities subject to a low-Mach grazing flow is revisited experimentally and theoretically. This instability is caused by the constructive feedback between the acoustic modes of the cavity and the turbulent shear layer that forms at its opening. Systematic experiments are performed in order to construct a new theoretical model, which describes the aeroacoustic system as two linearly stable oscillators, with linear reactive coupling, nonlinear damping and nonlinear resistive coupling. This model constitutes the basis for a linear stability analysis, and for the prediction of limit cycle amplitudes by using a describing function approach and by searching the fixed points of amplitude equations. Moreover, it is shown that only supercritical Hopf bifurcations are found in this aeroacoustic system, and that, in contrast with many flow-induced vibration problems, frequency lock-in does not occur. In the last part of the paper, the intermittency observed in the vicinity of the supercritical Hopf bifurcations is successfully modelled by adding a coloured multiplicative noise to the grazing flow velocity in order to account for the effect of turbulence. The necessary conditions favouring intermittently stable or intermittently unstable intervals in such systems are identified using stochastic differential equations governing the aeroacoustic oscillations and Fokker–Planck equations ruling the probability density function of the acoustic envelope. This work is relevant for many musical and industrial configurations exhibiting this type of aeroacoustic instability, as well as for thermoacoustic instabilities in turbulent combustors for aeronautic and power generation applications.

The dynamics of a cantilever plate clamped at its trailing edge and placed at a moderate angle ($\alpha \leq 30^{\circ }$) to a uniform flow are investigated experimentally and numerically, and a large experimental data set is provided. The dynamics are shown to differ significantly from the zero-angle-of-attack case, commonly called the inverted-flag configuration. Four distinct dynamical regimes arise at non-zero angles: a small oscillation around a small-deflection equilibrium (deformed regime), a small-amplitude flapping motion, a large-amplitude flapping motion and a small oscillation around a large-deflection equilibrium (deflected regime). The small- and large-amplitude flapping motions are shown to be produced by different physical mechanisms. The small-amplitude flapping motion appears gradually as the flow speed is increased and is consistent with a limit-cycle oscillation caused by the quasi-steady fluid forcing. The large-amplitude flapping motion is observed to appear at a constant critical flow speed that is independent of angle of attack. Its characteristics match those of the large-amplitude vortex-induced vibration present at zero angle of attack. The flow speed at which the plate enters the deflected regime decreases linearly as the angle of attack is increased, causing the flapping motion to disappear for angles of attack greater than $\alpha \approx 28^{\circ }$. Finally, the effect of aspect ratio on the plate dynamics is considered, with a plate of reduced aspect ratio being shown to lack a sharp distinction between flapping regimes for $\alpha >8^{\circ }$.

We report on direct numerical simulations of the effect of electrostatic charges on particle-laden duct flows. The corresponding electrostatic forces are known to affect the particle dynamics at small scales and the associated turbophoretic drift. Our simulations, however, predicted that electrostatic forces also dominate the vortical motion of the particles, induced by the secondary flows of Prandtl's second kind of the carrier fluid. Herein, we treated flows at two frictional Reynolds numbers ($Re_{\tau }= 300$ and 600), two particle-to-gas density ratios ($\rho _{p}/\rho =1000$ and 7500) and three Coulombic-to-gravitational force ratios ($F_{el}/F_{g}=0$, 0.004 and 0.026). In flows with a high density ratio at $Re_{\tau }=600$ and $F_{el}/F_{g}=0.004$, the particles tend to accumulate at the walls. On the other hand, at a lower density ratio, respectively a higher $F_{el}/F_{g}$ of 0.026, the charged particles still follow the secondary flow structures that are developed in the duct. However, even in this case, the electrostatic forces counteract the particles’ inward flux from the wall and, as a result, their vortical motion in these secondary structures is significantly attenuated. This change in the flow pattern results in an increase of the particle number density at the bisectors of the walls by a factor of five compared with the corresponding flow with uncharged particles. Finally, at $Re_{\tau }=300$, $\rho _{p}/\rho =1000$ and $F_{el}/F_{g}=0.026$ the electrostatic forces dominate over the aerodynamic forces and gravity and, consequently, the particles no longer follow the streamlines of the carrier gas.

During the last fifteen years there has been a paradigm shift in the continuum modelling of granular materials; most notably with the development of rheological models, such as the $\mu (I)$-rheology (where $\mu$ is the friction and I is the inertial number), but also with significant advances in theories for particle segregation. This paper details theoretical and numerical frameworks (based on OpenFOAM) which unify these currently disconnected endeavours. Coupling the segregation with the flow, and vice versa, is not only vital for a complete theory of granular materials, but is also beneficial for developing numerical methods to handle evolving free surfaces. This general approach is based on the partially regularized incompressible $\mu (I)$-rheology, which is coupled to the gravity-driven segregation theory of Gray & Ancey (J. Fluid Mech., vol. 678, 2011, pp. 353–588). These advection–diffusion–segregation equations describe the evolving concentrations of the constituents, which then couple back to the variable viscosity in the incompressible Navier–Stokes equations. A novel feature of this approach is that any number of differently sized phases may be included, which may have disparate frictional properties. Further inclusion of an excess air phase, which segregates away from the granular material, then allows the complex evolution of the free surface to be captured simultaneously. Three primary coupling mechanisms are identified: (i) advection of the particle concentrations by the bulk velocity, (ii) feedback of the particle-size and/or frictional properties on the bulk flow field and (iii) influence of the shear rate, pressure, gravity, particle size and particle-size ratio on the locally evolving segregation and diffusion rates. The numerical method is extensively tested in one-way coupled computations, before the fully coupled model is compared with the discrete element method simulations of Tripathi & Khakhar (Phys. Fluids, vol. 23, 2011, 113302) and used to compute the petal-like segregation pattern that spontaneously develops in a square rotating drum.

Galilean non-invariance of the shallow-water equations describing the motion of a rotating fluid implies that a homogeneous background flow modifies the dynamics of localized vortices even without the $\beta $-effect. In particular, in a divergent quasi-geostrophic model on a $\beta $-plane, which originates from the shallow-water model, the equation of motion in the reference frame attached to a uniform zonal background flow has the same form as in the absence of this flow, but with a modified $\beta $-parameter depending linearly on the flow velocity $\bar{U}$. The evolution of a singular vortex (SV) embedded in such a flow consists of two stages. In the first, quasi-linear stage, the SV motion is induced by the secondary dipole ($\beta $-gyres) generated in the neighbourhood of the SV. During the next, nonlinear stage, the SV merges with the $\beta $-gyre of opposite sign to form a compact vortex pair interacting with far-field Rossby waves radiated previously by the SV, while the other $\beta $-gyre loses connection with the SV and disappears. In the absolute reference frame and with $\beta = 0$, the SV drifts downstream and at an angle to the background flow. The SV always lags behind the background flow, with the strongest resistance during the quasi-linear stage and weakening resistance at the nonlinear stage of SV evolution. In the general case where $\beta \gt 0$, the SV can move both upstream (for small-to-moderate $\bar{U} \gt 0$) and downstream (for $\bar{U} \lt 0$ or sufficiently large $\bar{U} \gt 0$). Under weak-to-moderate westward and all eastward flows the SV cyclone (anticyclone) also moves northward (southward), its meridional drift increasing with $\bar{U}$.

The dynamics of initially truncated and bent line solitons for the Kadomtsev–Petviashvili (KPII) equation modelling internal and surface gravity waves is analysed using modulation theory. In contrast to previous studies on obliquely interacting solitons that develop from acute incidence angles, this work focuses on initial value problems for the obtuse incidence of two or three partial line solitons, which propagate away from one another. Despite counterpropagation, significant residual soliton interactions are observed with novel physical consequences. The initial value problem for a truncated line soliton – describing the emergence of a quasi-one-dimensional soliton from a wide channel – is shown to be related to the interaction of oblique solitons. Analytical descriptions for the development of weak and strong interactions are obtained in terms of interacting simple wave solutions of modulation equations for the local soliton amplitude and slope. In the weak interaction case, the long-time evolution of truncated and large obtuse angle solitons exhibits a decaying, parabolic wave profile with temporally increasing focal length that asymptotes to a cylindrical Korteweg–de Vries soliton. In contrast, the strong interaction case of slightly obtuse interacting solitons evolves into a steady, one-dimensional line soliton with amplitude reduced by an amount proportional to the incidence slope. This strong interaction is identified with the ‘Mach expansion’ of a soliton with an expansive corner, contrasting with the well-known Mach reflection of a soliton with a compressive corner. Interestingly, the critical angles for Mach expansion and reflection are the same. Numerical simulations of the KPII equation quantitatively support the analytical findings.