The flow behaviour of an inclined jet in crossflow (JICF) subjected to different upstream roughness regimes – smooth, transitionally rough (${k}_{s}/{D}=0.129$, where $k_{s}$ is the equivalent roughness height and $D$ is the jet hole diameter) and fully rough (${k}_{s}/{D}=0.782$) – is investigated using refractive-index-matching time-resolved particle image velocimetry for velocity ratios VR = 0.33, 0.67 and 1.0. The transitionally rough regime produces intensified, unbroken large-scale vortices that induce strong intermittency in the boundary-layer thickness. Its energy spectrum retains the original multi-scale coherence, but exhibits an additional wavelength associated with this intermittency. This intermittent state imposes the strongest unsteady influence on the downstream JICF, manifested as a binary flow pattern consisting of alternating jet lift-off and regular shedding. Time-averaged fields show a vertically elongated counter-rotating vortex pair (CRVP), while extended spectral proper orthogonal decomposition (ESPOD) indicates that the binary state drives modal bifurcation and distinct pathways associated with prematurely initiated centreline disturbance amplification. In contrast, the fully rough regime promotes rapid breakdown into small-scale turbulence. The ESPOD confirms that multi-scale frequency coherence decays rapidly, whereas low-frequency coherence experiences a brief amplification due to upstream signal injection. Additionally, secondary flows are observed to exert a localised, asymmetric modulation of the CRVP at VR ≤ 0.67: on the high-momentum pathway (downwash) side, one CRVP lobe is vertically compressed and its decay is delayed, while on the low-momentum pathway (upwash) side, the opposite lobe is vertically stretched and its decay is accelerated.

We investigate the equal-height, two-dimensional second-order structure function of the streamwise velocity fluctuation $u$ in turbulent channel flow. Specifically, at a given wall-normal location $z$ we consider $S_2(r_x,r_y;z)=\langle [u(x+r_x,y+r_y,z)-u(x,y,z)]^2\rangle$, where $(r_x,r_y)$ are the streamwise and spanwise separations in a wall-parallel plane and $\langle \boldsymbol{\cdot }\rangle$ denotes wall-parallel spatial averaging. Focusing on separations within the logarithmic region, we build on Townsend’s attached-eddy hypothesis and its hierarchical random additive-process formulation to introduce an attached-eddy elliptic approximation, in which the two-point geometry is represented by an elliptic in-plane footprint. The model yields a compact prediction for $S_2(r_x,r_y;z)$: its one-dimensional projections recover the canonical logarithmic forms with an asymptotically common slope, and its iso-$S_2$ contours at fixed $z$ are predicted to be self-similar ellipses whose semi-axes scale linearly with $z$ while maintaining an approximately constant aspect ratio (with mild finite-Reynolds-number effects). These predictions are assessed using direct numerical simulations at friction Reynolds numbers $Re_\tau =1000$ and $5200$, where $Re_\tau =u_\tau \delta /\nu$, and $u_\tau$ is the friction velocity, $\nu$ is the kinematic viscosity and $\delta$ is the channel half-height. When expressed in terms of $r_i/z$ ($i=x,y$), the projected structure functions collapse across wall-normal locations and vary linearly with $\ln (r_i/z)$. At fixed $z$, the iso-$S_2$ contours in the $(r_x,r_y)$ plane are well described by ellipses characterised by a single anisotropy parameter $R=b/a$, where $a$ and $b$ are the ellipse semi-axes in the $r_x$ and $r_y$ directions, respectively. A simple level-dependent parameterisation of $a$ and $b$ provides an accurate and parsimonious reconstruction of the two-dimensional fields. Collectively, these results establish a geometrically transparent and quantitatively predictive framework for the two-dimensional organisation of wall-attached motions in the logarithmic region, extending attached-eddy concepts beyond traditional one-dimensional formulations.

Direct numerical simulation (DNS) results of porous-wall turbulent flows in open channels with conjugate heat transfer are reported. For the conductive porous walls considered, the change in heat transfer is non-monotonic with permeability. The heat flux initially decreases when going from a conductive smooth wall to slightly porous walls. In this initial regime, the near-wall flow remains smooth-wall like and the heat transfer in the porous wall is dominated by molecular diffusion. A reduction of the more favourably conducting solid material then diminishes the heat transfer, whereas the skin friction monotonically increases with permeability. Beyond a certain permeability the near-wall flow transitions to the Kelvin–Helmholtz (K–H)-like regime (Gómez-de Segura & García-Mayoral 2019 J. Fluid Mech. 875, 124–172; Habibi Khorasani et al. 2024 J. Fluid Mech. 984, A63) with cross-stream rollers. The heat flux increases with permeability and eventually surpasses that of smooth-wall turbulence. Once in the K–H-like regime, turbulent heat transport can deeply penetrate the porous wall and be comparable to the turbulent heat transport in the channel region. Thermal performance is assessed in terms of the Reynolds analogy breakdown, which is the disparity between the fractional increases in the Stanton number, $ \textit{St}$, and the fractional increases in the skin-friction coefficient, $C_{\kern-1pt f}$, relative to smooth-wall flow (Bunker 2013 Proceedings of the ASME Turbo Expo 2013; Rouhi et al. 2022 J. Fluid Mech. 951, A45). Similar to rough walls, the breakdown is unfavourable for porous walls, which is due to growing dissimilarities between the transfer of momentum and heat near the porous wall as it becomes more permeable. Turbulent sweep and ejection events contribute more to momentum transfer than to heat transfer. However, unlike for rough walls, a saturation limit for heat transfer is not observed.

We study experimentally the detachment of a large pendant drop of non-Brownian monodisperse solid spheres in a Newtonian liquid, for high solid volume fractions ($0.55\leq \phi \leq 0.605$) compared with the critical volume fraction $\phi _{{c}}$ of the suspension. This set-up allows us to monitor both the bulk-effective deformation rate and the mean stress at the neck of the drop throughout detachment. The neck effective viscosity is found to decrease close to exponentially with the current neck radius, from a large initial value, $\eta _{{i}}$, down to the suspending liquid one. Experiments with different drop-to-particle size ratios indicate that, above $\phi _{{c}}$, the initial value $\eta _{{i}}$ is set by the viscosity-limited dilation of the particle phase. Observations on a transparent, doubly index-matched system reveal increasing deviation from axial symmetry and the collapse of capillary menisci at the drop interface during the exponential decay. A simplified model, based on the observed rheological evolution and the close-to-conical neck shape, captures the steeply accelerated detachment dynamics and shows how $\eta _{{i}}$ sets the breakup duration.

Bubbles rising in yield-stress fluids leave behind pathways in the memory of the fluid. These in turn influence the trajectories of subsequent bubbles released. Qualitatively, the effect manifests as a damaged pathway, modelled here as a low-viscosity Newtonian fluid within the surrounding viscoplastic fluid. Secondary bubbles are attracted towards these pathways, as is observed computationally and experimentally. Here we explore the effect of a damaged path on the release of a trapped bubble, captured by the critical yield number $Y_c$. We show that proximity to a damaged path increases $Y_c$, but eventually beyond a critical distance there is no influence on $Y_c$. We explore the effects of shape and surface tension on the aforementioned proximity results.

We investigate the orientation dynamics of a neutrally buoyant spheroid, of an arbitrary aspect ratio ($\kappa$), freely rotating in a weakly viscoelastic fluid undergoing simple shear flow. Weak elasticity is characterized by a small but finite Deborah number (${\textit{De}}$), and the suspending fluid rheology is therefore modelled as a second-order fluid, with the constitutive equation involving a material parameter $\epsilon$ related to the ratio of the first and second normal stress differences; polymer solutions correspond to $\epsilon \in [-0.7,-0.5]$. Employing a reciprocal theorem formulation, along with expressions for the relevant disturbance fields in terms of vector spheroidal harmonics, we obtain the spheroid angular velocity to $O(De)$. In the Newtonian limit, a spheroid rotates along Jeffery orbits parametrized by an orbit constant $C$, although this closed-trajectory topology is structurally unstable, being susceptible to weak perturbations. For ${\textit{De}}$ well below a threshold, ${\textit{De}}_c(\kappa )$, weak viscoelasticity transforms the closed-trajectory topology into a tightly spiralling one. A multiple-scales analysis is used to interpret the resulting orientation dynamics in terms of an $O(De)$ orbital drift. The drift in orbit constant over a Jeffery period $\Delta C$, when plotted as a function of $C$, identifies four different orientation dynamics regimes on the $\kappa -\epsilon$ plane. For $\epsilon$ in the polymeric range, prolate spheroids always drift towards the spinning mode. Oblate spheroids drift towards the tumbling mode for $\kappa \gt \kappa _c(\epsilon )$, but towards an intermediate kayaking mode for $\kappa \lt \kappa _c(\epsilon )$; $\kappa _c$ increases from $0.2$ to $0.454$ as $\epsilon$ varies from $-0.5$ to $-0.7$. The rotation of spheroids of extreme aspect ratios, either slender prolate spheroids ($\kappa \gg 1$) or thin oblate ones ($\kappa \ll 1$), about the vorticity axis, is arrested for ${\textit{De}} \geqslant {\textit{De}}_c(\kappa )$. The resulting rotation-arrested states exist within the flow-gradient plane in both cases, being nearly aligned with the flow direction for the prolate case, and oriented in the vicinity of the gradient direction for the oblate one. While rotation-arrested states are unstable to off-plane perturbations in the former instance, secondary bifurcations beyond the primary rotation-arrest threshold lead eventually to stable arrested states for thin oblate spheroids.