We investigate the intermittent dynamics of momentum transport and its underlying time scales in the near-wall region of the neutrally stratified atmospheric boundary layer in the presence of a vegetation canopy. This is achieved through an empirical analysis of the persistence time scales (periods between successive zero-crossings) of momentum flux events, and their connection to the ejection–sweep cycle. Using high-frequency measurements from the GoAmazon campaign, spanning multiple heights within and above a dense canopy, the analysis suggests that, when the persistence time scales ($t_p$) of momentum flux events from four different quadrants are separately normalized by $\varGamma _{w}$ (integral time scale of the vertical velocity), their distributions $P(t_p/\varGamma _{w})$ remain height-invariant. This result points to a persistent memory imposed by canopy-induced coherent structures, and to their role as an efficient momentum-transporting mechanism between the canopy airspace and the region immediately above. Moreover, $P(t_p/\varGamma _{w})$ exhibits a power-law scaling at times $t_{p}<\varGamma _{w}$, with an exponential tail appearing for $t_{p} \geq \varGamma _{w}$. By separating the flux events based on $t_p$, we discover that around 80 % of the momentum is transported through the long-lived events ($t_{p} \geq \varGamma _{w}$) at heights immediately above the canopy, while the short-lived ones ($t_{p} < \varGamma _{w}$) only contribute marginally ($\approx 20\,\%$). To explain the role of instantaneous flux amplitudes in momentum transport, we compare the measurements with newly developed surrogate data and establish that the range of time scales involved with amplitude variations in the fluxes tends to increase as one transitions from within to above the canopy.

Large-scale inertial particle clustering in a turbulent boundary layer (TBL) was investigated experimentally by two-colour particle-image velocimetry and particle-tracking velocimetry measurements in the wall-parallel plane of the log layer. The particle clusters were detected by Voronoi tessellation and a new application of a technique based on the spatial wavelet transform. Anisotropic wavelets spanning the range of measurable, large-scale particle clusters were applied to experimentally measured particle fields, and significance testing was used to identify hierarchies of particle clusters. Unlike the Voronoi tessellation, which primarily identified small-scale clusters, the wavelet technique also found a significant amount of anisotropic, large-scale clusters on the scale of the large-scale motions (LSMs) of the momentum field. The large-scale clusters were shown to be composed of a hierarchy of smaller clusters of varying degrees of isotropy. In addition to the cluster size distribution, the particle velocities within the clusters were studied as a function of cluster size. Larger clusters exhibited faster particle convection speeds, consistent with observations of the convection speeds of LSMs, thus providing additional evidence for the hypothesis that particles in the TBL accumulate on and are transported by large-scale, attached coherent structures.

We consider the Saintillan–Shelley kinetic model of active rod-like particles in Stokes flow (Saintillan & Shelley, Phys. Rev. Lett., vol. 100, issue 17, 2008a, 178103; Saintillan & Shelley, Phys. Fluids, vol. 20, issue 12, 2008b, 123304), for which the uniform isotropic suspension of pusher particles is known to be unstable in certain settings. Through weakly nonlinear analysis accompanied by numerical simulations, we determine exactly how the isotropic steady state loses stability in different parameter regimes. We study each of the various types of bifurcations admitted by the system, including both subcritical and supercritical Hopf and pitchfork bifurcations. Elucidating this system's behaviour near these bifurcations provides a theoretical means of comparing this model with other physical systems that transition to turbulence, and makes predictions about the nature of bifurcations in active suspensions that can be explored experimentally.

The wake flow past a streamwise rotating sphere is a canonical model of numerous applications, such as particle-driven flows, sport aerodynamics and freely rising or falling bodies, where the changes in particles’ paths are related to the destabilization of complex flow regimes and associated force distributions. Herein, we examine the spatio-temporal pattern formation, previously investigated by Lorite-Díez & Jiménez-González (J. Fluid Mech., vol. 896, 2020, A18) and Pier (J. Fluids Struct., vol. 41, 2013, pp. 43–50), from a dynamical system perspective. A systematic study of the mode competition between rotating waves, which arise from the linearly unstable modes of the steady-state, exhibits their connection to previously observed helical patterns present within the wake. The organizing centre of the dynamics turns out to be a triple Hopf bifurcation associated with three non-axisymmetric, oscillating modes with respective azimuthal wavenumbers $m=-1,-1$ and $-2$. The unfolding of the normal form unveils the nonlinear interaction between the rotating waves to engender more complex states. It reveals that for low values of the rotation rate, the flow field exhibits a similar transition to the flow past the static sphere, but accompanied by a rapid variation of the frequencies of the flow with respect to the rotation. The transition from the single helix pattern to the double helix structure within the wake displays several regions with hysteric behaviour. Eventually, the interaction between single and double helix structures within the wake lead towards temporal chaos, which here is attributed to the Ruelle–Takens–Newhouse route. The onset of chaos is detected by the identification of an invariant state of the normal form constituted by three incommensurate frequencies. The evolution of the chaotic attractor is determined using of time-stepping simulations, which were also performed to confirm the existence of bi-stability and to assess the fidelity of the computations performed with the normal form.

We investigate the retraction of a circular thin film coated with insoluble surfactants, which is punctured at its centre. We assume that the surface pressure of the liquid–gas interface is related to the number density of surfactants through a linear equation of state, which is characterized by a single parameter: the Gibbs dilation modulus. To solve the governing equations and track the deformation of the domain, we use the finite element method with an arbitrary Lagrangian–Eulerian approach where the film surface is sharp. Our simulations show that the surface elasticity introduced by the surfactants slows down the retraction and introduces oscillations at early times. In agreement with previous experiments and theoretical analysis, we find that the presence of surfactants introduces perturbations of the film thickness over progressively larger distances as the surface elasticity increases. The surface perturbations travel faster than the retracting edge of the film at a speed proportional to the Gibbs modulus. For large values of the Gibbs modulus, the interface behaviour approaches that of an incompressible two-dimensional solid. Our analysis sheds light on the effect of insoluble surfactants on the opening of a circular hole in a thin film and can be extended to investigate the onset of surface cracks and fractures.

The foundational differences of steady and unsteady jets issued into a laminar boundary layer crossflow are considered. Jets have been used widely for flow control applications, due to their ability to enhance mixing and mitigate separation, but it is unclear what role jet steadiness plays in flow control effectiveness. Here we compare experimentally unsteady (synthetic) and steady rectangular jets issued into a flat-plate laminar boundary layer with varying orifice pitch and skew. The coherent streamwise vortices produced by unsteady jets were shown to be much stronger than those produced by steady jets, despite producing similar flow patterns. These differences are rooted in how vorticity is generated in the orifice, through either a Stokes layer (unsteady) or a Blasius boundary layer (steady). Exploring the time- and phase-averaged vorticity transport equation reveals that the time-varying vorticity term is the reason for the enhanced vortical structure. When considering flow control metrics, we find that the unsteady jet produced greater added momentum in the boundary layer and added vorticity when compared to a momentum-matched steady jet. Both the steady and unsteady jets produced similar jet penetration characteristics.

A fluid multi-structure interaction (FMSI) study on flow-induced coupled vibrations of an elastically mounted cylinder and a detached flexible plate is carried out numerically at a constant $Re=100$. The effect of a non-dimensional gap $G^{*}$ between the two structures, and reduced velocity $U_{c}^{*}$, on the proximity-induced coupled flow physics and vibration characteristics of the system is presented. The FMSI system shows a two-state response: state 1 at larger gaps $G^{*}\geqslant 1$, and state 2 at smaller gaps $G^{*}\leqslant 0.5$. At larger $U_{c}^{*}$, the plate encounters an oscillating wake flow in state 1, while it encounters onset of gap flow in state 2. Each state relates to distinct vibration characteristics of both the structures, with the cylinder showing a vortex-induced vibration response in state 1 and a galloping response in state 2. The amplitude response of the cylinder is governed by gap flow dynamics while that of the plate is governed by the cylinder–plate vortex-interaction dynamics. In addition to the constructive and destructive vortex interactions reported earlier, a partial vortex interaction is observed here. The vortex interactions in the near wake lead to distinct vortex-shedding patterns – 2S, C(2S), 2P and a novel C(2P) – in the far wake. Separate regime maps are presented for the various types of cylinder–plate vortex interactions and vortex-shedding patterns, correlated with the amplitude, frequency and phase difference of the coupled vibrations of the cylinder and plate. The vortex dynamics shows a strong correlation with the quantitative vibration parameters, indicating the strongly coupled multi-physics characteristics of the present FMSI system.