Linearly stable shear flows first transition to turbulence in the form of localised patches. At low Reynolds numbers, these turbulent patches tend to suddenly decay, following a memoryless process typical of rare events. How far in advance their decay can be forecasted is still unknown. We perform massive ensembles of simulations of pipe flow and a reduced-order model of shear flows (Moehlis et al. 2004 New J. Phys. vol. 6, issues 1, p. 56) and determine the first moment in time at which decay becomes fully predictable, subject to a given magnitude of the uncertainty on the flow state. By extensively sampling the chaotic sets, we find that, as one goes back in time from the point of inevitable decay, predictability degrades at greatly varying speeds. However, a well-defined (average) rate of predictability loss can be computed. This rate is independent of the uncertainty and also of the type of rare event, i.e. it applies to decay and to other extreme events. We leverage our databases to define thresholds that approximately separate phase-space regions of distinct decay predictability. Our study has implications for the development of predictive models, in particular it sets their theoretical limits. It also opens avenues to study the causes of extreme events in turbulent flows: a state which is predictable to produce an extreme event is causal to it from a probabilistic perspective.

This study investigates the influence of free-stream turbulence (FST) and the thrust coefficient ($C_T$) on wind turbine wakes. Wakes generated at $C_T \in \{0.5, 0.7,0.9\}$ are exposed to turbulent inflows with varying FST intensities ($1\,\% \lesssim {\textit{TI}}_{\infty } \lesssim 11\,\%$) and integral length scales ($0.1 \lesssim {\mathcal L}_x/\!D \lesssim 2$, $D$ is the rotor diameter). For high-${\textit{TI}}_{\infty }$ inflows, a flow region in the wake is observed where a mean momentum deficit persists despite the turbulence intensity having already homogenised with that of the free stream, challenging traditional wake definitions. A ‘turning point’ in the mean wake width evolution is identified, beyond which wakes spread at slower rates. Near-field ($x\!/\!D \lesssim 7$) wake growth rate increases with higher ${\textit{TI}}_{\infty }$ and $C_T$, while far-field ($x\!/\!D \gtrsim 15$) wake growth rate decreases with higher ${\textit{TI}}_{\infty }$ – a finding with profound implications for wind turbine wake modelling that also aligns with the entrainment behaviours observed in bluff- and porous-body wakes exposed to FST. Increasing ${\mathcal L}_x$ delays wake recovery onset and reduces the mean wake width, with minimal effect on the spreading rate. Both $C_T$ and FST influence the high- and low-frequency wake dynamics, with varying contributions in the near and far fields. For low-${\textit{TI}}_{\infty }$ and small-${\mathcal L}_x$ inflows, wake meandering is minimal, sensitive to $C_T$ and appears to be triggered by a shear-layer instability. Wake meandering is enhanced for high-${\textit{TI}}_{\infty }$ and large-${\mathcal L}_x$ inflows, with the integral length scale playing a leading role. This emphasises the complex role of FST integral length scale: while increasing ${\mathcal L}_x$ amplifies meandering, it does not necessarily translate to larger mean wake width due to the concurrent suppression of entrainment rate.

We present an analysis of the coherent structures in Langmuir turbulence, a state of the ocean surface boundary layer driven by the interactions between water waves and wind-induced shear, via a resolvent framework. Langmuir turbulence is characterised by multiscale vortical structures, notably counter-rotating roll pairs known as Langmuir circulations. While classic linear stability analyses of the Craik–Leibovich equations have revealed key instability mechanisms underlying Langmuir circulations, the vortical rolls characteristic of Langmuir turbulence, the present work incorporates the turbulent mean state and varying eddy viscosity using data from large-eddy simulations (LES) to investigate the turbulence dynamics of fully developed Langmuir turbulence. Scale-dependent resolvent analyses reveal a new formation mechanism of two-dimensional circulating rolls and three-dimensional turbulent coherent vortices through linear amplification of sustained harmonic forcing. Moreover, the integrated energy spectra predicted by the principal resolvent modes in response to broadband harmonic forcing capture the dominant spanwise length scales that are consistent with the LES data. These results demonstrate the feasibility of resolvent analyses in capturing key features of multiscale turbulence–wave interactions in the statistical stationary state of Langmuir turbulence.

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.