In this work, we theoretically investigate the motion of an arbitrarily shaped particle in a linear density stratified fluid with weak stratification and negligible inertia. We calculate the hydrodynamic force and torque experienced by the particle using the method of matched asymptotic expansions. We analyse our results for two classes of particles (non-skew and skew) depending on whether the particle possesses a centre of hydrodynamic stress. For both classes, we derive general expressions for the modified resistance tensors in the presence of stratification. We demonstrate the application of our results by considering some specific examples of particles settling in a direction parallel to the density gradient by considering both the limits of high ($Pe\gg 1$) and low ($Pe\ll 1$) Péclet numbers. We find that presence of stratification causes a slender body to rotate and settle along the broader side due to the contribution of the hydrostatic torque. Our work sheds light on the impact of stratification on the transport of arbitrarily shaped particles in density stratified environments in low-Reynolds-number regimes.

Wall-resolved large-eddy simulations (LES) of the incompressible Navier–Stokes equations together with empirical modelling for turbulent Taylor–Couette (TC) flow are presented. LES were performed with the inner cylinder rotating at angular velocity $\unicode[STIX]{x1D6FA}_{i}$ and the outer cylinder stationary. With $R_{i},R_{o}$ the inner and outer radii respectively, the radius ratio is $\unicode[STIX]{x1D702}=0.909$. The subgrid-scale stresses are represented using the stretched-vortex subgrid-scale model while the flow is resolved close to the wall. LES is implemented in the range $Re_{i}=10^{5}{-}10^{6}$ where $Re_{i}=\unicode[STIX]{x1D6FA}_{i}R_{i}d/\unicode[STIX]{x1D708}$ and $d=R_{o}-R_{i}$ is the cylinder gap. It is shown that the LES can capture the salient features of the flow, including the quantitative behaviour of spanwise Taylor rolls, the log variation in the inner-cylinder mean-velocity profile and the angular momentum redistribution due to the presence of Taylor rolls. A simple empirical model is developed for the turbulent, TC flow for both a stationary outer cylinder and also for co-rotating cylinders. This consists of near-wall, log-like turbulent wall layers separated by an annulus of constant angular momentum. Model results include the Nusselt number $Nu$ (torque required to maintain the flow) and measures of the wall-layer thickness as functions of both the Taylor number $Ta$ and $\unicode[STIX]{x1D702}$. These are compared with results from measurement, direct numerical simulation and the LES. A model extension to rough-wall turbulent flow is described. This shows an asymptotic, fully rough-wall state where the torque is independent of $Re_{i}/Ta$, and where $Nu\sim Ta^{1/2}$.

This paper is concerned with steady-state subcritical gravity–capillary waves that are produced by potential flow past a wave-making body. Such flows are characterised by two non-dimensional parameters: the Froude number, $F$, and the inverse Bond number, $T$. When the size of the wave-making body is formally small, there are two qualitatively different flow regimes and thus a single bifurcation curve in the $(F,T)$ plane. If, however, the size of the obstruction is of order one, then, in the limit $F,T\rightarrow 0$, Trinh & Chapman (J. Fluid Mech., vol. 724, 2013, pp. 392–424) have shown that the bifurcation curve widens into a band, within which there are four new flow regimes. Here, we use results from exponential asymptotics to show how, in this low-speed limit, the water-wave equations can be asymptotically reduced to a single differential equation, which we solve numerically to confirm one of the new classes of waves. The issue of numerically solving the full set of gravity–capillary equations for potential flow is also discussed.

The extreme mobility of droplets on non-wetting materials implies the necessity of controlling their motion, direction or speed. In this paper, we show how ridges allow us to tune drop friction. Depending on the liquid speed and viscosity, two regimes emerge: fast drops with low viscosity dynamically deform and undergo inertial friction, so that their velocity is eventually fixed by the deformations induced by the ridges; in contrast, viscous drops hardly interact with the texture, so that their velocity is classically limited by viscous dissipation, as on a flat substrate. The transition between these two regimes reveals spectacular morphological changes: drops with intermediate viscosity elongate and adopt worm-like shapes, which we qualitatively describe.

The linear and nonlinear dynamics of an interface separating a thin liquid film and a hydrodynamically passive ambient medium, subject to normal electrostatic forcing, are investigated. A reduced-order model is developed for the case where both fluids are taken to be leaky dielectrics (LD). Cases of time periodic as well as steady forcing are studied. In the former case, an important result is the elucidation of two forms of resonant instability than can occur in LD films. These correspond to an inertial resonance due to mechanical inertia of the fluid and an inertialess resonance due to charge capacitance at the interface that is similar to mechanically forced films with an insoluble surfactant. In the case of steady forcing, the long-time dynamics exhibits spontaneous sliding as the interface approaches the wall, for the two limiting cases of a perfect conductor–perfect dielectric pair as well as a pair of perfect dielectrics. Under these limits, only the normal component of the Maxwell stress at the interface is significant and the interface dynamics resembles that of a Rayleigh–Taylor unstable interface. For a general pair of leaky dielectrics studied in the limit of fast relaxation times, the presence of interfacial charge prevents the onset of sliding. For the special case when the square of the conductivity ratio equals the permittivity ratio, the interface exhibits cascading structures, similar to those reported for the long-wave Marangoni instability.

Direct numerical simulation of the Navier–Stokes equations has been used to investigate the Taylor–Couette flow with an imposed pulsatile axial pressure gradient resulting in a spiral Poiseuille flow modulated by an oscillating forcing. Keeping the Reynolds and Taylor numbers constant, both the amplitude and frequency of the oscillating component are varied to span a small region of the phase space. In the narrow-gap geometry considered in this study, the base flow (spiral Poiseuille flow) is in the turbulent regime whereas the oscillating component is laminar. It has been found that the effect of the oscillation is to induce a global flow laminarization provided the frequency is sufficiently small (at constant amplitude) or the amplitude is sufficiently large (at constant frequency). The coupling between steady and oscillating components has been analysed with the help of long-time and phase-averaged statistics. The reverse transition mechanism has been associated to an anisotropic modification of the Reynolds stress tensor components, which has been shown to be caused by an alteration of the pressure–strain interaction.

An inviscid flow model is presented to gain a basic understanding of the reflection of a swept oblique shock from a planar wall. The analytical model is constructed to describe the fundamental influence of sweep on this shock configuration, which has been commonly studied as an unswept non-dimensional shock boundary layer interaction (SBLI). Transformation of model parameters into a plane perpendicular to the sweep angle reduces the resultant flow to a two-parameter system. An equivalency between this configuration and others commonly assessed is presented with advisory notes on the definition of effective coordinate systems. Inviscid shock detachment has been associated with the onset of quasi-conical SBLI spanwise development; see (Settles & Teng, AIAA J., vol. 22 (2), 1984, pp. 194–200). Its occurrence for this SBLI configuration is determined for a range of conditions and compared to experimental observations of swept SBLIs claiming cylindrical/conical similarity scalings. Finally, influence of a zero-mass flux plane associated with typical experimental and numerical analyses is presented with an accompanying model for the shock structure. While this paper serves as a useful resource when designing swept impinging oblique SBLI studies, it also provides a vital benchmark for this complex configuration and helps to unify various SBLI configurations that are often analysed in isolation.

In this paper we derive unsteady tri-periodic laminar solutions of the Navier–Stokes equations. In particular, these represent fully three-dimensional (3-D) flows, since all the velocity components depend non-trivially on all three coordinate directions. We show that they belong to the class of Beltrami flows and can be gathered in two distinct solutions characterized by positive and negative helicity. These can be regarded as an extension in three dimensions of the bi-periodic vortex solution by Taylor (Phil. Mag., vol. 46, 1923, pp. 671–674). Their use as benchmarks for checking the accuracy of 3-D numerical codes and/or studying the onset of turbulence is suggested.