We present a theoretical study, supported by simulations and experiments, on the spreading of a silicone oil drop under MHz-frequency surface acoustic wave (SAW) excitation in the underlying solid substrate. Our time-dependent theoretical model uses the long-wave approach and considers interactions between fluid dynamics and acoustic driving. While similar methods have analysed the micron-scale oil and water film dynamics under SAW excitation, acoustic forcing was linked to boundary layer flow, specifically Schlichting and Rayleigh streaming, and acoustic radiation pressure. For the macroscopic drops in this study, acoustic forcing arises from Reynolds stress variations in the liquid due to changes in the intensity of the acoustic field leaking from the SAW beneath the drop and the viscous dissipation of the leaked wave. Contributions from Schlichting and Rayleigh streaming are negligible in this case. Both experiments and simulations show that, after an initial phase where the oil drop deforms to accommodate acoustic stress, it accelerates, achieving nearly constant speed over time, leaving a thin wetting layer. Our model indicates that the steady speed of the drop results from the quasi-steady shape of its body. The drop speed depends on drop size and SAW intensity. Its steady shape and speed are further clarified by a simplified travelling-wave-type model that highlights various physical effects. Although the agreement between experiment and theory on drop speed is qualitative, the results’ trend regarding SAW amplitude variations suggests that the model realistically incorporates the primary physical effects driving drop dynamics.

Turbulent wall-bounded flows, although present in many practical applications, are particularly challenging to simulate because of their large velocity gradients near the walls. To avoid the necessity of an extremely fine mesh resolution in the near-wall regions of wall-bounded turbulent flows, large eddy simulation (LES) with specific modelling near the wall can be applied. Since filtering close to the boundaries of the flow domain is not uniquely defined, existing wall-modelled LES typically rely on extensive assumptions to derive suitable boundary conditions at the walls, such as assuming that the instantaneous filtered velocity behaves similarly to the unfiltered mean velocity. Volume filtering constitutes a consistent extension of filtering close to the boundaries of the flow domain. In the present paper, we derive a formally exact expression for the wall-boundary conditions in LESs using the concept of volume filtering applied to wall-bounded turbulent flows that does not make any a priori assumptions on the flow field. The proposed expression is an infinite series expansion in powers of the filter width. It is shown in an a priori study of a turbulent channel flow and an a posteriori study of the turbulent flow over periodic hills that the proposed expression can accurately predict the volume-filtered velocity at the wall by truncating the infinite series expansion after a few terms.

We consider the two-layer quasi-geostrophic model with linear bottom friction and, in certain simulations, a planetary vorticity gradient, $\beta$. We derive energy budgets in wavenumber space for eddy available potential energy (EAPE), baroclinic eddy kinetic energy (EKE) and barotropic EKE, a particular decomposition that has previously been overlooked. The conversion between EAPE and baroclinic EKE, $\widehat {T}^{{W}}$, has a strong dependence on both bottom drag strength and planetary $\beta$. At the deformation scale $\widehat {T}^{{W}}$ is always negative, representing the conversion of EAPE to EKE via baroclinic instability. For strong, linear bottom drag, $\widehat {T}^{{W}}$ is positive at large scales due to frictional energisation of the baroclinic mode, providing a large-scale EAPE source. With weak-to-moderate bottom drag and moderate-to-strong planetary $\beta$, $\widehat {T}^{{W}}$ is the dominant source of EAPE at large scales, converting baroclinic EKE that has experienced a baroclinic inverse cascade back into EAPE, and thus closing a novel and exclusively baroclinic energy loop. With planetary $\beta$, zonal jets form and the dominant large-scale processes in the energy cycle of the system, e.g. barotropic dissipation and the peak of positive $\widehat {T}^{{W}}$, occur at the meridional wavenumber corresponding to the jet spacing, with no zonal wavenumber component, i.e., $k_{x}=0$. Importantly, the traditional source of large-scale EAPE, barotropic stirring of the baroclinic mode, is not a part of this $k_{x} = 0$ energy cycle, and thus plays a secondary role. The results suggest that consideration of horizontally two-dimensional processes is requisite to understand the energetics and physics of baroclinic geophysical jets.

Robust surfaces capable of reducing flow drag, controlling heat and mass transfer, and resisting fouling in fluid flows are important for various applications. In this context, textured surfaces impregnated with a liquid lubricant show promise due to their ability to sustain a liquid–liquid interface that induces slippage. However, theoretical and numerical studies suggest that the slippage can be compromised by surfactants in the overlying fluid, which contaminate the liquid–liquid interface and generate Marangoni stresses. In this study, we use Doppler-optical coherence tomography, an interferometric imaging technique, combined with numerical simulations to investigate how surfactants influence the slip length of lubricant-infused surfaces with longitudinal grooves in a laminar flow. Surfactants are endogenously present in the contrast agent (milk) which is added to the working fluid (water). Local measurements of slip length at the liquid–liquid interface are significantly smaller than theoretical predictions for clean interfaces (Schönecker & Hardt 2013). In contrast, measurements are in good agreement with numerical simulations of fully immobilized interfaces, indicating that milk surfactants adsorbed at the interface are responsible for the reduction in slippage. This work provides the first experimental evidence that liquid–liquid interfaces within textured surfaces can become immobilised in the presence of surfactants and flow.

We use the theory of spectral submanifolds (SSMs) to develop a low-dimensional reduced-order model for plane Couette flow restricted to the shift–reflect invariant subspace in the permanently chaotic regime at ${Re}=187.8$ studied by Kreilos & Eckhardt (2012, Chaos: Interdisciplinary J. Nonlinear Sci., vol. 22, 047505). Our three-dimensional model is obtained by restricting the dynamics to the slowest mixed-mode SSM of the edge state. We show that this results in a nonlinear model that accurately reconstructs individual trajectories, representing the entire chaotic attractor and the laminar dynamics simultaneously. In addition, we derive a two-dimensional Poincaré map that enables the rapid computation of the periodic orbits embedded in the chaotic attractor.

We investigate the dynamics of an oscillatory boundary layer developing over a bed of collisional and freely evolving sediment grains. We perform Euler–Lagrange simulations at Reynolds numbers ${\textit{Re}}_\delta = 200$, 400 and 800, density ratio $\rho _{\!p}/\rho _{\!f} = 2.65$, Galileo number ${\textit{Ga}} = 51.9$, maximum Shields numbers from $5.60 \times 10^{-2}$ to $2.43 \times 10^{-1}$, based on smooth wall configuration, and Keulegan–Carpenter number from $134.5$ to $538.0$. We show that the dynamics of the oscillatory boundary layer and sediment bed are strongly coupled due to two mechanisms: (i) bed permeability, which leads to flow penetration deep inside the sediment layer, a slip velocity at the bed–fluid interface, and the expansion of the boundary layer, and (ii) particle motion, which leads to rolling-grain ripples at ${\textit{Re}}_\delta = 400$ and ${\textit{Re}}_\delta = 800$. While at ${\textit{Re}}_\delta = 200$ the sediment bed remains static during the entire cycle, the permeability of the bed–fluid interface causes a thickening of the boundary layer. With increasing ${\textit{Re}}_\delta$, the particles become mobile, which leads to rolling-grain ripples at ${\textit{Re}}_\delta = 400$ and suspended sediment at ${\textit{Re}}_\delta = 800$. Due to their feedback force on the fluid, the mobile sediment particles cause greater velocity fluctuations in the fluid. Flow penetration causes a progressive alteration of the fluid velocity gradient near the bed interface, which reduces the Shields number based upon bed shear stress.

Wakes and the dynamic interactions of multiple wakes have been a focal point of numerous research endeavours. Traditionally, wake interaction studies have focused on wakes produced by similar bodies. In contrast, the present study positions a non-shedding porous disc adjacent to periodically shedding solid discs of varying diameters and dimensional shedding frequencies. Using hot-wire measurements, we explore the intriguing interaction between these wakes. Remarkably, our findings reveal that the wake of the non-shedding disc acquires oscillations from the wake of the shedding disc, irrespective of their distinct frequencies. We demonstrate high receptivity of the porous disc’s wake and connect our findings to real-life applications.

The inertial migration of neutrally buoyant spherical particles in viscoelastic fluids flowing through square channels is experimentally and numerically studied. In the experiments, using dilute aqueous solutions of polymers with various concentrations that have nearly constant viscosities, we measured the distribution of suspended particles in downstream cross-sections for the Reynolds number ($\textit{Re}$) up to 100 and the elasticity number ($El$) up to 0.07. There are several focusing patterns of the particles, such as four-point focusing near the centre of the channel faces on the midlines for low $\textit{El}$ and/or high $\textit{Re}$, four-point focusing on the diagonals for medium $\textit{El}$, single-point focusing at the channel centre for relatively high $\textit{El}$ and low $\textit{Re}$, and five-point focusing near the four corners and the channel centre for high $\textit{El}$ and very low $\textit{Re}$. Among these focusing patterns, various types of particle distributions suggesting the presence of a new equilibrium position located between the midline and the diagonal, and multistable states of different equilibrium positions were observed. In general, as $\textit{El}$ increases from 0 at a constant $\textit{Re}$, the particle focusing positions shift from the midline to the diagonal in the azimuthal direction first, and then inward in the radial direction to the channel centre. These focusing patterns and their transitions were numerically well reproduced based on a FENE-P model with measured values of viscosity and relaxation time. Using the numerical results, the experimentally observed focusing patterns of particles are elucidated in terms of the fluid elasticity-induced lift and the wall-induced elastic lift.