Three-dimensional laminar flow over an inclined spinning disk is investigated at a Reynolds number of ${\textit{Re}} = 500$ and an angle of attack of $\alpha = 25^\circ$, for tip-speed ratios up to 3. Numerical simulations are performed to investigate the effect of spin on the aerodynamics and characterise the instabilities that occur. Increasing tip-speed ratio significantly increases both lift and drag monotonically. Several distinct wake regimes are observed, including vortex shedding in the non-spinning case, vortex-shedding suppression at moderate tip-speed ratios and a distinct corkscrew-like short-wavelength instability in the advancing tip vortex at higher tip-speed ratios. Vorticity generated by the spinning disk strengthens the advancing tip vortex, inducing a spanwise stretching in the trailing-edge vortex sheet. This helps to dissipate the vorticity, which in turn prevents roll up and suppresses vortex shedding. The short-wavelength instability shows qualitative and quantitative matches to the $(-2,0,1)$ principal mode of the elliptic instabilities seen in pairs of counter-rotating Batchelor vortices. The addition of vorticity from the disk rotation significantly alters the circulation and axial velocity in the tip vortices, giving rise to elliptic instability despite its absence in the non-spinning case. In select cases, lock-in between the frequency of the elliptic instability and twice the spin frequency is observed, indicating that disk rotation acts as an additional forcing for the elliptic instability. Additional simulations at different Reynolds numbers and angle of attacks are considered to examine the robustness of observed phenomena across different parameter combinations.

The Monin–Obukhov similarity theory (MOST) is a cornerstone of atmospheric science for describing turbulence in stable boundary layers. Extending MOST to stably stratified turbulent channel flows, however, is non-trivial due to confinement by solid walls. In this study, we investigate the applicability of MOST in closed channels and identify where and to what extent the theory remains valid. A key finding is that the ratio of the half-channel height to the Obukhov length serves as a governing parameter for identifying distinct flow regions and determining their corresponding mean velocity scaling. Hence, we propose a relation to estimate this ratio directly from the governing input parameters: the friction Reynolds and friction Richardson numbers ($\textit{Re}_{\tau }$ and $Ri_{\tau }$). The framework is tested against a series of direct numerical simulations across a range of $\textit{Re}_{\tau }$ and $Ri_{\tau }$. The reconstructed velocity profiles enable accurate prediction of the skin-friction coefficient crucial for quantifying pressure losses in stratified flows in engineering applications.

In this paper, we numerically investigate the orbit dynamics of three-dimensional symmetric Janus drops in shear flow using an improved ternary-fluids phase field method, focusing on how drop deformation and initial orientation affect the orbit drift of two configurations of Janus drops: dumbbell-shaped and near-spherical. We find that the motion of dumbbell-shaped drops eventually evolves into tumbling, while near-spherical drops attain stable spinning. We attribute this bifurcation in orbit drift to contrasting deformation dynamics and shape-dependent hydrodynamics of the two configurations. Specifically, the drift bifurcation is closely related to the aspect ratio of Janus drops at equilibrium, giving rise to two distinct mechanisms: (1) coupling between outer interface deformation and the surrounding flow field; and (2) interplay between inner interface deformation and vortices enclosed within the drop. In addition, we observe that for the dumbbell-shaped Janus drops with different aspect ratios, their tumbling dynamics resembles ellipsoids in shear flow. Moreover, the trajectories of the dumbbell-shaped Janus drops during orbit drift collapse onto a universal curve, independent of their initial orientations, and significant deformation and inertia accelerate the orbit transition. To quantitatively evaluate the effect of drop deformation on the orbit drift of the dumbbell-shaped Janus drops, we propose an effective aspect ratio model based on the drop shapes at equilibrium and at the maximum elongation. By incorporating the effective aspect ratio into Jeffery’s theory for solid particles, we accurately predict the rotation period and angular velocity of Janus drops in the tumbling regime and during the orbit drift, especially for drops with linear deformation. Moreover, the orbit parameter $C$ is found to vary exponentially with time for drops with linear deformation, while the time variation of $C$ transits from one exponential function to another for drops with nonlinear deformation.

The thermal interactions of liquid droplets impacting a moving substrate are investigated, combining theoretical modelling with experimental validation. An analytical model is developed to predict the time-evolving contact temperature and heat flux at the droplet–substrate interface. Accounting for the convective heat transport induced by the impacting drop, the model incorporates a finite thermal contact resistance, which is a critical parameter that was often neglected in earlier studies for drop impact. High-speed, spatially resolved infrared thermography is used to record the two-dimensional, transient temperature evolution at the droplet–substrate interface during drop impact on a rotating disc. Measured temperature maps are used for numerical simulations to reconstruct local interfacial heat fluxes. The model is validated for different droplet diameters, substrate velocities and thermal conditions. The findings demonstrate that the substrate velocity and droplet diameter have negligible influence on the thermal behaviour within the tested parameter space.

The deposition of droplets onto a swollen polymer network induces the formation of a wetting ridge at the contact line. Current models typically consider either viscoelastic effects or poroelastic effects, while polymeric gels often exhibit both properties. In this study, we investigate the growth of the wetting ridge using a comprehensive large-deformation theory that integrates both dissipative mechanisms – viscoelasticity and poroelasticity. In the purely poroelastic case, following an initial instantaneous incompressible deformation, the growth dynamics exhibits scale-free behaviour, independent of the elastocapillary length or system size. A boundary layer of solvent imbibition between the solid surface (in contact with the reservoir) and the region of minimal chemical potential is created. At later times, the ridge equilibrates on the diffusion time scale given by the elastocapillary length. When viscoelastic properties are incorporated, our findings show that, during the early stages (prior to the viscoelastic relaxation time scale), viscoelastic effects dominate the growth dynamics of the ridge and solvent transport is significantly suppressed. Beyond the relaxation time, the late-time dynamics closely resembles that of the purely poroelastic case. These findings are discussed in light of recent experiments, showing how our approach offers a new interpretation framework for wetting of polymer networks of increasing complexity.

The two-dimensional (2-D) evolution of perturbed long weakly nonlinear surface plane, ring and hybrid waves, consisting, to leading order, of a part of a ring and two tangent plane waves, is modelled numerically within the scope of the 2-D Boussinesq–Peregrine system. Numerical runs are initiated and interpreted using the reduced 2-D cylindrical Korteweg–de Vries (cKdV)-type and Kadomtsev–Petviashvili II (KPII) equations. The cKdV-type equation leads to two different models, the KdV$\theta$, where $\theta$ stands for a polar angle, and cKdV equations, depending on whether we use the general or singular (i.e. the envelope of the general) solution of the associated nonlinear first-order differential equation. The KdV$\theta$ equation is also derived directly from the 2-D Boussinesq–Peregrine system and used to analytically describe the intermediate 2-D asymptotics of line solitons subject to sufficiently long transverse perturbations of finite strength, while the cKdV equation is used to initiate outward- and inward-propagating ring waves with localised and periodic perturbations. Both of these equations, together with the KPII equation, are used to model the evolution of hybrid waves, where we show, in particular, that large localised waves (lumps) can appear as transient (emerging and then disappearing) states in the evolution of inward-propagating waves, contributing to the possible mechanisms for the generation of rogue waves. Detailed comparisons are made between the key features of the non-stationary 2-D modelling and relevant predictions of the reduced equations.

In this work, we study the reaction-controlled dual bubbles ripening on a heterogeneous substrate with high surface wettability hysteresis, where the bubbles evolve with constant contact radius but varied contact angle. We first theoretically derived the governing kinetic equation of bubble curvature radius $R_B$, based on which we surprisingly found three possible ripening processes under six different conditions, i.e. the classical Ostwald ripening (the bubble with the larger curvature radius $R_B$ exhibits an increase in $R_B$, while the bubble with the smaller curvature radius $R_B$ experiences a decrease in $R_B$), the reversed ripening (converse to Ostwald ripening), and the consistent ripening ($R_B$ of both bubbles increases or reduces consistently). Further analyses from the aspects of chemical potential and free energy lead to an interesting finding that the $R_B$ of two bubbles finally reach egalitarianism, independently of different ripening processes. Numerical results obtained from two-phase lattice Boltzmann modelling demonstrate excellent agreement with theoretical predictions, specifically concerning the kinetic equation, the various ripening processes, and the egalitarianism of bubble radii $R_B$ after ripening completion.

This study investigates the dynamics of free-surface turbulence (FST) using direct numerical simulations (DNS). We focus on the energy exchange between the deformed free-surface and underlying turbulence, examining the influence of high Reynolds (${\textit{Re}}$) and Weber (${\textit{We}}$) numbers at low to moderate Froude (${\textit{Fr}}$) numbers. The two-fluid DNS of FST at the simulated conditions is able to incorporate air entrainment effects in a statistical steady state. Results reveal that a high ${\textit{We}}$ number primarily affects entrained bubble shapes (sphericity), while ${\textit{Fr}}$ significantly alters free-surface deformation, two-dimensional compressibility and turbulent kinetic energy (TKE) modulation. Vortical structures are mainly oriented parallel to the interface. At lower ${\textit{Fr}}$, kinetic energy is redistributed between horizontal and vertical components, aligning with rapid distortion theory, whereas higher ${\textit{Fr}}$ preserves isotropy near the surface. Evidence of a reverse or dual energy cascade is verified through third-order structure functions, with upscale transfer near the integral length scale, and enhanced vertical kinetic energy in upwelling eddies. Phase-based discrete wavelet transforms of TKE show weaker decay at the smallest scales near the interface, suggesting contributions from gravitational energy conversion and reduced dissipation. The wavelet energy spectra also exhibits different scaling laws across the wavenumber range, with a $-3$ slope within the inertial subrange. These findings highlight scale- and proximity-dependent effects on two-phase TKE transport, with implications for subgrid modelling.

In this experimental study, we investigate, for the first time, the structure and evolution of the near wake of a circular cylinder in a flowing soap film at the onset of vortex shedding. The study primarily focuses on the changes occurring within the recirculation bubble, along with the evolution of vortex shedding. A significantly large recirculation bubble forms behind the cylinder in the soap film environment, characterized by small-scale vortices along its edges, an observation that starkly contrasts with its three-dimensional counterparts. These small-scale vortices driven by the Kelvin–Helmholtz instability, further induce a transverse deflection of the recirculation bubble, leading to an intermittent generation of the wake vortices. The instantaneous velocity field in the wake is examined, highlighting the clear evidence of intermittency in vortex formation. The frequency and wavelength of the chain of small-scale vortices on the recirculation bubble is evaluated, and a functional relationship with the flow Reynolds number is determined. We believe this observation to be novel, potentially revealing a new pathway for understanding the two-dimensional transition in bluff-body wakes.