Hydrodynamic density functional theory (DFT) is applied to analyse dynamic contact angles of droplets to assess its predictive capability regarding wetting phenomena at the microscopic scale and to evaluate its feasibility for multiscale modelling. Hydrodynamic DFT incorporates the influence of fluid–fluid and solid–fluid interfaces into a hydrodynamic theory by including a thermodynamic model based on classical DFT for the chemical potential of inhomogeneous fluids. It simplifies to the isothermal Navier–Stokes equations far away from interfaces, thus connecting microscopic molecular modelling and continuum fluid dynamics. In this work, we use a Helmholtz energy functional based on the perturbed-chain statistical associating fluid theory (PC-SAFT) and the viscosity is obtained from generalised entropy scaling, a one-parameter model which takes microscopic information of the fluid and solid phase into account. Deterministic (noise-free) density and velocity profiles reveal wetting phenomena including different advancing and receding contact angles, the transition from equilibrium to steady state and the rolling motion of droplets. Compared with a viscosity model based on bulk values, generalised entropy scaling provides more accurate results, which stresses the importance of including microscopic information in the local viscosity model. Hydrodynamic DFT is transferable as it captures the influence of different external forces, wetting strengths and (molecular) solid roughness. For all results, good quantitative agreement with non-equilibrium molecular dynamics simulations is found, which emphasises that hydrodynamic DFT is able to predict wetting phenomena at the microscopic scale.

Wall-resolved large-eddy simulations of flow over an axisymmetric body of revolution (DARPA SUBOFF bare model) at $ \it{Re}_L=1.1\times 10^6$ are performed to investigate wall pressure fluctuations under the combined effects of transverse curvature and varying pressure gradients. Due to the coexistence of convex and concave streamwise curvatures, the flow in the stern region features alternating zones of favourable and adverse pressure gradients (APGs). The simulation validates experimental findings by Balantrapu et al. (2023, J. Fluid Mech., vol. 960, A28), confirming that in APG-dominant axisymmetric boundary layers without streamwise curvatures, the root mean square wall pressure fluctuations ($p_{w,rms}$) decrease downstream alongside the wall shear stress ($\tau _w$), maintaining a constant ratio $p_{w,rms}/\tau _{w}$. This study further finds that when streamwise curvatures and strong streamwise pressure gradient variations present, this relationship breaks down, suggesting that $\tau _w$ is not the dominant contributor to wall pressure fluctuations. Instead, the local maximum Reynolds shear stress $-\rho \langle u_su_n\rangle _{max }$ emerges as a more robust pressure scaling parameter. Normalising the wall pressure spectra by $-\rho \langle u_su_n\rangle _{max }$ yields better collapse across the entire stern region compared to conventional inner or mixed scaling methods. The magnitude and location of $-\rho \langle u_su_n\rangle _{max }$ significantly influence the spectral levels of wall pressure fluctuations across different frequency bands. As the turbulence intensity and $-\rho \langle u_su_n\rangle _{max }$ shift away from the wall, outer-layer structures – with larger spatial and temporal scales – dominate the coherence of wall pressure fluctuations. This mechanism drives sustained attenuation of high-frequency pressure fluctuations and a simultaneous increase in both the streamwise and transverse correlation lengths of wall pressure fluctuations over the stern region.

Recently, Nagib et al. (Phys. Fluids, vol. 36, no. 7, 2024, 075145) used indicator functions of streamwise normal stress profiles to identify the valid wall-distance and Reynolds number ranges for two models in direct numerical sumulation (DNS) of channel and pipe flows. Since such functions are challenging to construct from experimental data, we propose a simpler, more robust method better suited to experiments. Applied to the two leading models – logarithmic and power-law – for normal stresses in the ‘fitting region’ of wall-bounded flows, this method is tested on prominent experimental data sets in zero-pressure-gradient (ZPG) boundary layers and pipe flows across a wide Reynolds number range ($Re_\tau$). Valid regions for the models appear only for $Re_\tau \gtrapprox 10{\,}000$, with a lower bound $y^+_{in} \sim (Re_\tau )^{0.5}$ and $y^+_{in} \gtrapprox 400$. The upper bound is a fixed fraction of the boundary layer thickness or pipe radius, independent of $Re_\tau$. The power-law model is found to hold over a broader range, up to $Y \approx 0.4$ in ZPG and $Y \approx 0.5$ in pipe flows, compared with the logarithmic trend, which is formulated to be coincident with the classical logarithmic region for the mean flow ($Y \lessapprox 0.15$). A slightly higher exponent ($0.28$) than that of Chen & Sreenivasan (J. Fluid Mech. vol. 933, 2022, A20; J. Fluid Mech. vol. 976, 2023, A21) extends the power-law model’s validity and correcting for outer intermittency in ZPG flows further broadens it. Projections to the near-wall region of both models yield nearly identical predictions of near-wall peak stress across the highest available $Re_\tau$. These findings, alongside results from Monkewitz & Nagib (J. Fluid Mech. vol. 967, 2023, A15) and Baxerras et al. (J. Fluid Mech. vol. 987, 2024, R8), highlight the importance of nonlinear eddy growth and residual viscous effects in wall-bounded flow modelling, informing potential refinements to the logarithmic model, such as those proposed by Deshpande et al. (J. Fluid Mech. vol. 914, 2021, A5).

Rayleigh–Taylor instability (RTI) caused by rarefaction waves not only features variable acceleration but also incorporates time-dependent density, which introduces great challenges in predicting the finger growth behaviours. In this work, we propose a model for predicting the single-mode finger behaviours by extending the Layzer potential-flow framework to account for time-dependent acceleration and density. Relative to the previous models, the present model can evaluate the effect of time-dependent density on finger growth, and can describe the growth behaviours of both bubbles and spikes in rarefaction-driven RTI flows. In addition, the time-dependent curvature of the finger tip as it evolves from its initial value to the quasi-steady value is quantified. To validate the model, rarefaction-tube experiments and numerical simulations are conducted across a wide range of initial conditions. The results show that the present model can accurately capture the amplitude growth and curvature evolution of bubbles and spikes across various density ratios. Moreover, both the present model and experiments demonstrate that the continuous density reduction in rarefaction-driven flows causes larger asymptotic velocities of bubbles and spikes, leading to higher Froude numbers relative to those under constant or time-dependent acceleration.

This study uses the diffusion analogy (Miyake, Sci. Rep., 5R-6, 1965, Univ. of Washington, Seattle, USA) to predict the full growth behaviour of internal boundary layers (IBLs) induced by a roughness change for neutrally – and especially stably – stratified boundary layers with finite thickness. The physics of the diffusion analogy shows that the streamwise variation of the IBL thickness is dictated by $\sigma _w/U$ at the interface, where $\sigma _w$ and $U$ represent wall-normal Reynolds stress and mean streamwise velocity, respectively. The existing variants of the model, summarised by Savelyev & Taylor (2005, Boundary-Layer Meteorol., vol. 115, pp. 1–25), are tailored to IBLs confined within the constant shear stress layer. To extend the applicability of the model to the outer region, we investigate the relation between $\sigma _w/U$ and $U/U_\infty$ in the outer region across varying stratification, where $U_\infty$ is the free-stream velocity. Our analysis reveals that wind tunnel data from a number of facilities collapse onto a master curve when $\sigma _w/U$ is premultiplied by a height-independent parameter, which is a function of the ratio of Monin–Obukhov length to the boundary layer thickness. The scaled $\sigma _w/U$ decreases inversely with $U/U_\infty$ in the surface layer, transitioning to a linear decrease as $U/U_\infty$ increases. The new model, which integrates these findings, along with the effects of streamline displacement and acceleration, captures the complete characteristics of IBLs as they develop within turbulent boundary layers of finite thickness.

Turbulent flows exhibit large intermittent fluctuations from inertial to dissipative scales, characterised by multifractal statistics and breaking the statistical self-similarity. It has recently been proposed that the Navier–Stokes turbulence restores a hidden form of scale invariance in the inertial interval when formulated for a dynamically (nonlinearly) rescaled quasi-Lagrangian velocity field. Here we show that such hidden self-similarity extends to the large-eddy-simulation (LES) approach in computational fluid dynamics (CFD). In particular, we show that classical subgrid-scale models, such as implicit or explicit Smagorinsky closures, respect the hidden scale invariance at all scales – both resolved and subgrid. In the inertial range, they reproduce the hidden scale invariance of Navier–Stokes statistics. These properties are verified very accurately by numerical simulations and, beyond CFD, turn LES into a valuable tool for fundamental turbulence research.

We present a theoretical framework for porous media gravity currents propagating over rigid curvilinear surfaces. By reducing the flow dynamics to low-dimensional models applicable on surfaces where curvature effects are negligible, we demonstrate that, for finite-volume releases, the flow behaviour in both two-dimensional and axisymmetric configurations is primarily governed by the ratio of the released viscous fluid volume to the characteristic volume of the curvilinear surface. Our theoretical predictions are validated using computational fluid dynamics simulations based on a sharp-interface model for macroscopic flow in porous media. In the context of carbon dioxide geological sequestration, our findings suggest that wavy cap rock geometries can enhance trapping capacity compared with traditional flat-surface assumptions, highlighting the importance of incorporating realistic topographic features into subsurface flow models.

In this work, we study the effectiveness of the time-localised principal resolvent forcing mode at actuating the near wall cycle of turbulence. This mode is restricted to a wavelet pulse and computed from a singular value decomposition of the windowed wavelet-based resolvent operator (Ballouz et al. 2024b, J. Fluid Mech. vol. 999, A53) such that it produces the largest amplification via the linearised Navier–Stokes equations. We then inject this time-localised mode into the turbulent minimal flow unit at different intensities, and measure the deviation of the system’s response from the optimal resolvent response mode. Using the most energetic spatial wavenumbers for the minimal flow unit – i.e. constant in the streamwise direction and once-periodic in the spanwise direction – the forcing mode takes the shape of streamwise rolls and produces a response mode in the form of streamwise streaks that transiently grow and decay. Though other works such as Bae et al. (2021 J. Fluid Mech. vol. 914, A3) demonstrate the importance of principal resolvent forcing modes to buffer layer turbulence, none instantaneously track their time-dependent interaction with the turbulence, which is made possible by their formulation in a wavelet basis. For initial times and close to the wall, the turbulent minimal flow unit matches the principal response mode well, but due to nonlinear effects, the response across all forcing intensities decays prematurely with a higher forcing intensity leading to faster energy decay. Nevertheless, the principal resolvent forcing mode does lead to significant energy amplification and is more effective than a randomly generated forcing structure and the second suboptimal resolvent forcing mode at amplifying the near-wall streaks. We compute the nonlinear energy transfer to secondary modes and observe that the breakdown of the actuated mode proceeds similarly across all forcing intensities: in the near-wall region, the induced streak forks into a structure twice-periodic in the spanwise direction; in the outer region, the streak breaks up into a structure that is once-periodic in the streamwise direction. In both regions, spanwise oscillations account for the dominant share of nonlinear energy transfer.

The breakup dynamics of viscous liquid bridges on solid surfaces is studied experimentally. It is found that the dynamics bears similarities to the breakup of free liquid bridges in the viscous regime. Nevertheless, the dynamics is significantly influenced by the wettability of the solid substrate. Therefore, it is essential to take into account the interaction between the solid and the liquid, especially at the three-phase contact line. It is shown that when the breakup velocity is low and the solid surface is hydrophobic, the dominant channel of energy dissipation is likely due to thermally activated jumping of molecules, as described by the molecular kinetic theory. Nevertheless, the viscous dissipation in the bulk due to axial flow along the bridge can be of importance for long bridges. In view of this, a scaling relation for the time dependence of the minimum width of the liquid bridge is derived. For high viscosities, the scaling relation captures the time evolution of the minimum width very well. Furthermore, it is found that external geometrical constraints alter the dynamic behaviour of low and high viscosity liquid bridges in a different fashion. This discrepancy is explained by considering the dominant forces in each regime. Lastly, the morphology of the satellite droplets deposited on the surface is qualitatively compared with that of free liquid bridges.

A model is proposed for the one-dimensional spectrum and streamwise Reynolds stress in pipe flow for arbitrarily large Reynolds numbers. Constructed in wavenumber space, the model comprises four principal contributions to the spectrum: streaks, large-scale motions, very-large-scale motions and incoherent turbulence. It accounts for the broad and overlapping spectral content of these contributions from different eddy types. The model reproduces well the broad structure of the premultiplied one-dimensional spectrum of the streamwise velocity, although the bimodal shape that has been observed at certain wall-normal locations, and the $-5/3$ slope of the inertial subrange, are not captured effectively because of the simplifications made within the model. Regardless, the Reynolds stress distribution is well reproduced, even within the near-wall region, including key features of wall-bounded flows such as the Reynolds number dependence of the inner peak, the formation of a logarithmic region, and the formation of an outer peak. These findings suggest that many of these features arise from the overlap of energy content produced by both inner- and outer-scaled eddy structures combined with the viscous-scaled influence of the wall. The model is also used to compare with canonical turbulent boundary layer and channel flows, and despite some differences being apparent, we speculate that with only minor modifications to its coefficients, the model can be adapted to these flows as well.

Yaw control can effectively enhance wind farm power output, but the vorticity distribution and coherent structures in yawed turbine wakes remain poorly understood. We propose a physical model capable of accurately predicting tip vortex dynamics from their generation to destabilisation. This model integrates a point vortex framework with advanced blade element momentum theory and vortex cylinder theory for yawed turbines. Comparisons with large eddy simulations demonstrate that the model effectively predicts the vorticity distribution of tip vortices and the wake profile of yawed turbines. Finally, we employ sparsity-promoting dynamic mode decomposition to analyse the dynamics of the far wake. Our analysis reveals four primary mode types: (i) the averaged mode; (ii) shear modes; (iii) harmonic modes; and (iv) merging modes. Under yawed conditions, these modes become asymmetric, leading to interactions between the tip and root vortex modes. This direct interaction plays a critical role during the formation process of the counter-rotating vortex pair observed in yawed wakes.

Linear hydroelastic waves propagating in a frozen channel are investigated. The channel has a rectangular cross-section, finite depth and infinite length. The liquid in the channel is an inviscid, incompressible liquid and covered with ice. The ice is modelled as a thin elastic plate of variable thickness clamped to the channel walls. The thickness is constant along the channel length and varying across it. The flow induced by ice deflections is potential. The problem reduced to a problem of wave profiles across the channel and was solved using a piecewise linear approximation of a shape of the thickness. Normal modes are calculated to ensure continuous deflections, slopes, bending stresses and shear forces in the ice plate. Two thickness distributions are studied: in Case I, the thickness is constant at a middle segment and linearly increases at edge segments over the channel’s width; in Case II, the thickness linearly decreases at the edge segments. In Case I, there is one segment with the thin part of the ice cover where, as expected, the oscillations of the ice plate will be concentrated. In Case II, there are two such areas, separated by the middle segment with the thick part of the ice cover. Dispersion relations, phase and group velocities, wave profiles and strain distributions in the ice plate are studied. Results show that the properties of periodic hydroelastic waves are significantly influenced by the ice thickness distribution across the channel.

We investigate the effect of streamwise and transverse rotation on the wake behind an elastically mounted sphere. Simulations are performed at a Reynolds number $Re=500$ over a range of reduced velocity $2\le U^{\ast }\le 12$, considering a low and high rotational speed (0.2 and 1), keeping the mass ratio $m^{\ast }=2$. Streamwise rotation yields a structural response akin to the non-rotating case, while transverse rotation triggers induced vibration at lower $U^{\ast }$ and sustains it across a wider range. Like the non-rotating case, the streamwise rotating sphere exhibits synchronous, high-amplitude vibration across the entire $U^\ast$ range, whereas for low transverse rotation, it is confined to $5\le U^{\ast }\le 6$. Cross-stream displacement of the sphere remains unaffected by streamwise rotation with increasing $U^{\ast }$. In contrast, it monotonically increases due to transverse rotation, driven by the Magnus force, as supported by our theoretical and numerical estimations. While the spiral shedding mode dominates at $\Omega _{x}=0.2$, twisted hairpin and twisted spiral modes emerge as the rotation rate is increased. On the other hand, we observe the hairpin (HP) mode, as seen in the non-rotating case, for low transverse rotation. The HP mode gives rise to the ring vortical mode at the far wake, and with an increase in $U^\ast$, the wake shows small-scale stretched threads and reconnected bridgelets. Wake fluctuations increase with a streamwise rotation that saturates at higher $U^{\ast }$ during synchronisation, while desynchronisation at dimensionless transverse rotation rate $\Omega _{z}=1$ induces intermittent low-amplitude vibration via the Magnus effect. Space–time reconstruction at the near wake shows an undisturbed helical vortex core at $\Omega _{x}=0.2$ and $U^{\ast }=5$, which bifurcates at $\Omega _{x}=1$ owing to the centrifugal-induced distortion. At $\Omega _{x}=1$ and $U^{\ast }=5$, the phase difference between $(y, C_{y})$ and $(z, C_{z})$ exhibits in-phase synchrony with occasional phase slips. The wake vortex remains unaffected by the transverse rotation of the sphere; however, a streamwise rotating sphere couples the wake, leading to a rotational lock-in. The wake rotation shifts from anti-clockwise to clockwise sense earlier (in $U^\ast$) at a lower rotation rate. The reduced velocity is seen to have a favourable effect on the transfer of the sphere’s rotational inertia onto the wake as the measured penetration depth increases with $U^{\ast }$. Insights from the present research will aid in understanding complex flow interactions in rotational systems, improving efficiency, stability and control in modern engineering applications.